Point Spread Function Research Papers

Phase-retrieved pupil functions in wide-field fluorescence microscopy

by David Agard

2004, Journal of Microscopy

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Blind Deconvolution for Confocal Laser Scanning Microscopy

by Praveen Pankajakshan

2010

Figure 4.8: 2, normalized estimated PSFs obtained from the blind decon- volution algorithms compared with the given analytical model (©)Ariana-INRIA/13S). over estimates it. If we increase the number of iterations of the MLEM blind approach, eventually the PSFs tend to disappear completely favoring the Dirac solution. This was discussed at the beginning of Subsection 2.2 and is also shown in Chapter 5. In literature, denoising was applied as a prior step as a form of regularization on the object. It was mentioned that this approach is not recom- mended because there is no known relationship that models the resulting data to the original observation. In our experiments, we verified that for the same num- ber of iterations of the naive MLEM BD, denoising before BD over estimates the FWHM of the PSF than the regular approach (cf. Fig. 4.8).

the final IDIV(o|o) between o in Fig. 4.9(a) and 0 in (c) is 1.4334. Fig. 4.11(a) compares the estimated 3D PSF with the analytically modeled PSF in Eq. (3.52) and the best 3D Gaussian fit (in the least-squared sense) for the analytical model. The PSFs are shown along one direction of an off-central lateral plane, and the highlighted section of the plot can be viewed in the inset. The maximum of the residual error between the estimate and the true PSF is displayed on a logarith- mic contrast stretch in Fig. 4.11(b). As is evident from the log of the residue, the Gaussian model does not capture the side lobes in the analytical model, and yet

histograms for the observed image volume and the volume after the background was subtracted. When we compare the histograms, we observe how the entire his- togram has been shifted towards the zero after the background subtraction (BS). What we can also infer from the background estimated section is that there is a uniformity in the illumination and no alignment problems. The mean value of the background signal from this estimation procedure was found to be about 3.13 IU. Next, the overall histogram of the image volume, in Fig. 1.6, was smoothed IU. Next, the overall histogram of the image volume, in Fig. 1.6, was smoothed tribution was estimated to be lie between 3.9683 and 3.9702 IU with a 95% confi-

[1999]), which calculates the proportion of observed peak intensity at the detec- As explained in Chapter 3, their £; norms satisfy the following constraints:

Figure 4.16: Observed root apex of an Arabidopsis Thaliana with a volume 146.448 um x 146.448um x 30.222um (INRA). The sub- volume chosen for restoration is emphasized.

— igure 5.8: The experimental set-up schematic for generating spherical aberra- tion due to refractive index mismatch when imaging point sources (©)Ariana-INRIA /13S).

The above equality is possible iff each of the individual terms within the sum are ters @, and @, are assumed to be known or a priori estimated as describe in the

These microspheres, manufactured by Invitrogen», have a specified nominal di ameter of 15um. Molecular Probes® uses its proprietary fluorescent dye tech nology to produce these polystyrene spheres coated with a fluorescent dye. Th fluorescence of the sample can be measured by exciting the dye at a specific wave length and recording the emission light at their respective maximum emissio1 wavelengths. Since these dyes have a penetration depth between 500 —700nm and on emission, they resemble a spherical shell. These images are very handy be cause the object viewed has a definite geometry and size. In Fig. 4.13(a), we shov cause the object viewed has a definite geometry and size. In Fig. 4.13(a), we show the raw data that is Nyquist sampled at 89.26nm along the lateral and 232.75nm along the optic axis. The excitation peak wavelength, in this case, is 488nm and emission is at 520nm. The backprojected pinhole size is 1AU and no line averag- ing was done during the acquisition process. The total size of the image stack 1s 256 x 256 x 130 voxels or 22.85 x 22.85 x 30.03 um. The objective lens used is an oil immersion ‘Plan Apochromat’ with NA 1.4 and 63x magnification. Although the geometry of this test sample is nice, as the RI of the sphere is in general not the same as that of the embedding media, they also degrade the PSF. In particu- lar, when viewing the central plane, those rays approaching the focus from the direction of the center of the sphere will be highly aberrated and will produce

much fainter concentric circular rings (see Fig. 1.2). This example of diffraction is of great importance because many optical instruments (including the human eye) have circular apertures. If this smearing of the image of a point source is larger than that produced by the aberrations of the system, the imaging process is said to be diffraction-limited, and that is the best resolution which can be obtained from that size of aperture. As the objective constitutes an important part of CLSM, the quality of the image, and its resolution is dependent on the quality of the lens used, its numerical aperture (NA), and the wavelength of excitation light used.

Figure 3.1: An illustration of coherent, monochromatic light as an electromag- netic wave. The electric and magnetic fields oscillate at directions orthogonal to the propagation of the light (©)Ariana-INRIA/I3S). where yu, is the permeability, and ¢,,, is the permittivity of the medium. V x E gives the curl of E, and V-«,,,E gives the divergence of E. If the medium is homo- geneous, €,, 1s constant throughout the region of propagation. The medium is said to be non-dispersive to light if €,,, is independent of the wavelength A of the light used. All media are nonmagnetic hence the permeability of the medium is the same as that in vacuum.

ion). As the water/specimen index of refraction is different from the index of and with the specimen in water (cf. Kam, et al. [2007] for setup with AO correc-

there is no saturation or clipping of intensities. The mean and the variance of the dark current image were estimated using a maximum likelihood (ML) estimate. The mean of the background signal was about 22.35% intensity units (IU) and variance 16.98. When the gain is minimum, the mean was found to be 5.2482+ 5% IU and variance 7.25. In practice, the dark noise can be minimized by cooling the detector tube. Under non-ideal imaging conditions, there is another type of noise generated as a result of the dark current. Dark current occurs due to thermionic emissions in the dynodes, leakage currents, field emissions, electronic emission by cosmic rays and sometimes stray indoor illuminations. Although very small, if the detector gain is large, its contribution to the final signal is significant. This dark noise N, has an average dark flux gj, and Ny ~ P(qgz). Fig. 1.4(a) shows the signal observed in a Zeiss LSM 510 microscope when there is no excitation source, with PMT gain adjusted to get the dynamic range, and when it is operating in the “photon counting mode”. The detector gain and the offset are set so that the ‘photon counting mode”. The detector gain and the offset are set so that the

Figure 2.2: Histograms of the numerical gradients for four different confocal pinhole settings (©)Ariana-INRIA/I3S). variational (TV) regularization functional (cf, Rudin, et al. [1992]):

lence. Since the object fluorescence was sparsely populated, we find that there is 1ot much difference between the mean estimates by considering the overall vol- ime or the individual section. This is valid in most of the images taken using _CLSM where the object fluorescence is sparse throughout the volume. How- ver, We notice a significant difference between the background estimated using he dark image with full amplifier gain and the above estimation for an observed olume. This reinforces the idea that the background needs to be estimated for very observation volume, and if the object fluorescence is sparse, the estimation ould be carried out on the observation. For more details on homogenous or 1eterogenous background estimation in fluorescence microscopy, the interested eader may refer to the following articles by van Kempen & van Vliet [2000] and chen, et al. [2006].

for H(k,,) exists and the analytical expression can be written as Proof. It is simple to show that differentiation of (x) with respect to x is

Figure 2: Annual scientific citations for the subject of deconvolution and blind deconvolution. (Data source: ISI web of knowledge).

theoretically calculated PSF in Eq. (3.52) can be written as

Figure 4.3: Gamma distribution for three different pairs of shape and scaling parameters ((¢)Ariana-INRIA /I3S). Eq. (4.24) leads to a noninformative Jeffreys hyperprior. Using the hyperprio:

|.2 Fundamental Limits in Imaging The optical system of a microscope is inherently diffraction limited (Pawley [2006]; Born & Wolf [1999]) and the image of a point source, the point-spread function (PSF), displays a lateral diffractive ring pattern (expanding with defocus) introduced by the finite-lens aperture. This is because when light from a point source passes through a small circular aperture, it does not produce a bright dot as an image, but rather a diffused circular disc known as Airy disc surrounded by

Figure 3.8: Plot of the Bessel function of first kind with order zero. As the function’s power is raised, the side lobes becomes smaller and so does the FWHM of the central maxima.

$correct SA PSF. It can be seen that the observed intensity profile is axially shifted from the true axial position by about 8 slices. After restoration with the SA PSF, the estimated object’s axial location corresponds very well with the true position of the object. The intensity profile is quite symmetrical in comparison to the observed profile. However, when restoration is done using a diffraction-limited approximation (ignoring aberrations), it led to error in the actual axial position. We can also observe that the intensity is highly asymmetrical and is worse than the observation profile.$

corresponds to the true radial microsp (0) very precise lateral locations (%°, y precise lateral locations (£;’, 93 tation of the observation data in Fig. 5.2 due to focal anomaly the axial relative lo rately obtained from the observation da here position. The above method gives For example, Fig. 5.3 shows the segmen- c) by using the above method. However, ° a(O 3 cation (a )) of the object cannot be accu- ta. In the example given above, the COG of the observation, the nominal position was accurately estimated as 8 slices off the central plane. However, this does not correspond with the actual position of the object in the volume.

shown in Fig. 3.4. Eqs. (3.23) and (3.24) are known as the “sine condition” and

Figure 1.3: Aberrated wavefront at the exit pupil. (©)Ariana-INRIA /I3S). also through the specimen before it is detected. In Fig. 1.3, we show the aberrated

where the numerical forward and backward derivatives are defined as

mated. Using Bayes’ postulate, a uniform distribution 1s assumed for the initial

-, in Tab. 2.2, is a small positive constant that bounds the higher frequencies anc

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Efficient scatter correction using asymmetric kernels

by Gary Virshup

2009, Progress in Biomedical Optics and Imaging - Proceedings of SPIE

X-ray cone-beam (CB) projection data often contain high amounts of scattered radiation, which must be properly modeled in order to produce accurate computed tomography (CT) reconstructions. A well known correction technique is the scatter... more

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Digital camera imaging system simulation

by Dmitry Bakin

2009, Electron Devices, …

A digital camera is a complex system including a 4 lens, a sensor (physics and circuits), and a digital image processor, 5 where each component is a sophisticated system on its own. Since 6 prototyping a digital camera is very expensive,... more

Fig. 8. MTF comparison. Data measured from the captured one versus the simulated images at 300 1x for the MT9TO12 sensor. Ny marks the percentage of drop at the Nyquist frequency.

Fig. 3. (Red) Estimated versus (green) actual spectral reflectance for 24 patches of a color checker.

Fig. 9. Relative illumination comparison of the captured one versus the simulated images at 300 Ix for the MT9TO12 sensor. Value taken from row 510 of the image pair shown in Fig. 10(a).

Fig. 2. Response curves for the Canon EOS-1Ds Mark II camera with a 50-mm EF USM f/1.4 lens. The calculation was performed per color channel on the Canon raw data. The curves are obtained for each channel and plotted by each prime color. They almost sit on top of each other.

Fig. 5. Illustration of a sensor crosstalk. (Left) Optical crosstalk. (Right) Electrical crosstalk. The incoming light already converges by the microlens. It shows how the signal intended for the center red pixel to get crosstalked into the neighboring green pixels optically and electrically.

Fig. 1. Camera model. A camera is modeled as a cascaded system of optics, a sensor, and a digital image processor. The sensor is modeled as a series of filtering (the infrared filter, the color filter array, and the pixel QE) followed by a sampling of the sensor grid, where signal crosstalk happens simultaneously. Junging Chen, Member, IEEE, Kartik Venkataraman, Dmitry Bakin, Brian Rodricks, Robert Gravelle, Pravin Rao, and Yongshen Ni

Fig. 4. Optics distortions: (Left) Barrel and (right) pincushion distortion. 244 There are various formulas to calculate f., for example

Fig. 10. Comparison of the captured one versus the simulated images at 10 and 300 Ix. The images at 10 lx were cropped out with 100% zoom. The MT9T012 sensor was used. (a) Captured at 300 Ix. (b) Simulated at 300 Ix. (c) Captured at 10 1x (100% zoom). (d) Simulated at 10 lx (100% zoom).

Fig. 7. (Left) Micron MT9TO12 sensor QE of the sensor along with the transmission curves for filters used to obtain narrow-band light sources. The figure on the right shows the signal captured by the sensor. Each color channel output is plotted with its prime color.

Fig. 6. Crosstalk experiment setup illustration. Two rotational axes and the CRA are marked.

Fig. 10. Comparison of the captured one versus the simulated images at 10 and 300 Ix. The images at 10 lx were cropped out with 100% zoom. The MT9TO17 sensor was used. (a) Captured at 300 Ix. (b) Simulated at 300 Ix. (c) Captured at 10 1x (100% zoom). (d) Simulated at 10 lx (100% zoom).

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Phase retrieval using coherent imaging systems with linear transfer functions

by Marcus Kitchen

2004, Optics Communications

We consider the problem of quantitative phase retrieval from images obtained using a coherent shift-invariant linear imaging system whose associated transfer function (i.e., the Fourier transform of the complex point-spread function) is... more

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Blurred image restoration: A fast method of finding the motion length and angle

by Libor Machala and

2010, Digital Signal Processing

Motion blur in photographic images is a result of camera movement or shake. Methods such as Blind Deconvolution are used when information about the direction and size of blur is not known. Restoration methods, such as Lucy and Richardson... more

Fig. 11. Captured images blurred by camera shake (left) and the corresponding results of restoration using the parameters estimated by our algorithn (right).

MSE for the results of restoration with/without a gradient computation. Table 1

Fig. 9. MSE dependence in case of noise for SNR = 40 dB (Signal-to-Noise Ratio) and without noise using 10 iterations of the Lucy-Richardson algorithm.

Fig. 12. PSF kernels corresponding to the above three images.

Fig. 10. The advantage of our reconstruction (LR method) in comparison to inverse filtering method suggested by [19] in the presence of noise, SNR = 40 dB

The projection (sum) of the (filtered) gradient power spectrum along the estimated angle a is called the target function The target function, illustrated in Fig. 4, carries information about the distance between stripes in the gradient powe! spectrum which is related to the blur length. The method of inferring the blur length by identifying the dominant frequency contained within the target function by means of the one-dimensional Fourier transform was intended at the beginning. Unfortunately, due to the noise in rea (camera shaken) images this approach seemed to be unreliable in approximately half of the cases.

Fig. 5. Example: Test image blurred, L =7 pixels, 0 = 45 degrees (left) and the corresponding result of restoration using the parameters estimated by our algorithm (20 iterations) (right).

Fig. 8. Blurred image of Lena and result of restoration, blur parameters: L=9, © = 45 degrees.

Fig. 6. The dependence of MSE for the results of restoration with/without a gradient computation.

Fig. 2. Logarithm of the power spectrum of the image gradient in the frequency domain and the filtered power spectrum The whole process of deblurring can be briefly summarized into the following steps (see Fig. 1):

Fig. 7. Typical characteristics of MSE dependence on the length of blur using 10, respectively 20 iterations of the Lucy-Richardson algorithrr

Fig. 1. The reconstruction process — main ideas. an accurate estimation of the blur kernel, whic image reconstructions of fluorescence microgra h is considered as radially symmetric. Krishnamurthi [16] accomplished real phs by using a blind-deconvolution algorithm based on maximum-likelihood estimation. Other deblurring algorithms with isotropic PSF [9] or a three-dimensional (3-D) separable Gaussian PSF [10] were tested on computed tomography (CT) images. Sakano [12] suggested an algorithm based on the Hough transform which can accurately and robustly estimate the motion b applied method of inverse filtering and discrete that was most likely with respect to the distri ur PSF, even in low signal-to-noise ratio cases. Al Maki and Sugimoto [19 sine transform. As a non-blind method, Fergus [20] estimated the blur kernel bution of a possible latent (original) image. However, the user must specify an image region without saturation effects. Sroubek et al. [25] used multiple photographs to estimate the blur kernel and to reconstruct the image. Here, we present a fast method of determining the angle and size of blur from a single photograph, which enables to construct a correct PSF kernel.

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On the complex three-dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography

by Tristan Colomb

2007, Journal of Microscopy

The point spread function is widely used to characterize the three-dimensional imaging capabilities of an optical system. Usually, attention is paid only to the intensity point spread function, whereas the phase point spread function is... more

We have considered here the case of an incident field linearly polarized in the x direction, but the expressions could be generalized for any arbitrary polarization state (Mansuripur, 2002). Even if the incident field had a component only along the x direction, the field at the focal plane will have components along all the three directions x (unit vector i), y (unit vector j) and z (unit vector k) (Fig. 2) and for a specific position can be calculated as follows (Gu, 2000): Fig. 2. Vectorial model: focusing ofa linearly polarized (x direction) beam through a lens of focal length f, half-aperture a, maximum subtended half angle a.

Fig. 4. APSF computed in the axial direction with the vectorial model for a x 63/0.85 MO (a) and a x 100/1.3 MO (b). The intensity distributions are enhanced by a nonlinear distribution of the grey levels, the phase distributions are coded in 8 bits between —z = black and +z = white.

Fig. 1. Scalar Debye theory: focusing of a spherical wave through a lens of focal f, half-aperture a, maximum subtended half angle a. The Debye theory combines in this way the geometrical and the wave optics, because all the individual plane waves

Fig. 9. Temporal phase fluctuations at CCD1, CCD2, and the phase difference between the to phases (1000 holograms recorded in 40 s).

Fig. 8. (a) Example of an experimental 512 x 512 8-bits hologram; (b) a z00m, corresponding to the dashed square of (a), where the interference fringes appear more visible; (c) the Fourier spectrum of (a) containing the zero order (zo), the real image (ri), the virtual image (vi) and also parasitic interferences spatial frequencies (p); (d) Fourier spectrum after application of the bandpass filter.

Fig. 10. Axial APSF (amplitude and phase) for different cover slip thickness compensation in an adjustable collar x20 0.4 NA microscope objective: collar at position O (a), 0.5 (b) and 1 (c). The insets enhance the phase singularities appearing at the zero intensity points. The intensity distributions are enhanced by a nonlinear distribution of the grey levels, the phase distributions are coded in eight bits between —z = black and z = white.

Fig. 3. The x-, y- and z-components of the vectorial transverse APSF (xy) for a x 63/0.85 MO. ly: ly: 1;, are in proportion of, respectively, 1: 0.0032: 0.1290. Calculations were performed on a 4 x 4 mm? surface in the xy plane for all the component. The intensity distributions are normalized, the phase distributions are coded between —z = black and +z = white.

Fig. 7. Experimental setup for the APSF measurement: BS beam-splitter, BE beam expander, NF neutral density filter, 4/2 half-wave plate, M mirror, FC fibre coupling lens, PS piezo system, MS micrometric stage, MO microscope objective, O object wave, R reference wave. Inset: a detail showing the off-axis geometry at the incidence on the CCD. Our setup is based on a Mach-Zehnder interferometer configuration. In the object arm, a point-source object is imaged through the MO or through the lens to characterize. (Fig. 7). As a point source we use a near field scanning optical microscopy (NSOM) fibre, with a 60-nm-diameter emitting tip. The light source is a A = 532 nm laser (frequency-doubled Nd: YAG) with adjustable power up to 100 mW and the laser is coupled in the optical fibre by a lens. The MO is mounted on micrometric xyz platforms combined with tilt facilities, allowing for proper alignment of the MO to avoid aberrations coming from the setup misalignment. Fine fibre movements, are achieved by a piezoelectric xyz stage, which permits nanometric displacements (1 step = 1.22 nm, within arange of 80 wm). ACCD camera (CCD1) is positioned at a large distance of about 1500 mm to create a sufficiently high magnification (about 1000x for a 100x MO) image of the point object,

Fig. 6. Axial profiles through the xz section of the IPSF and PPSF for the x 100/1.30 MO, without (a) and with (b) spherical aberrations induced by the use of nondesigned parameters (cover slip, immersion oil). A linear phase corresponding to the displacement along the optical axis has been subtracted in both (a) and (b) to enhance the anomalous phase behaviour in presence of aberration.

Fig. 11. Axial (a) and radial (b) comparisons in amplitude and phase between experimental APSF measurement (up) and calculated APSF with the Gibson and Lanni model [10] for a x 100 1.3 NA microscope objective. Measurements performed in oil (n = 1.518) without cover slip. The intensity distributions are enhanced by a nonlinear distribution of the grey levels, the phase distributions are coded in 8 bits between —z = black and z = white.

Fig. 5. Axial APSF (xz) examples when the cover slip and the immersion oil refractive index are varied according to Gibson model: ideal case ng = 1.525, ni = 1.518 (a), cover slip refractive index is varied ng = 1.530 (b), immersion oil refractive index is varied ni = 1.514 (c). The MO considered here was x 100/1.30. The intensity distributions are enhanced by a nonlinear distribution of the grey levels, the phase distributions are coded in eight bits between —z = black and +z = white. Aberrations are present in most optical imaging systems: lenses, lenses assembly and MO. They are generally a consequence of the fabrication process; spherical aberrations in particular are due to grinding and polishing process of the lens which naturally tends to produce spherical surfaces. These aberrations are usually compensated by the recourse to the assembly of several lenses having complementary geometrical and dielectriccharacteristics. Other types ofaberrations appear when the focused beam crosses one or several dielectric layers, for which the MO has not been designed. To analyze the aberrations appearing when a MO is used under inappropriate conditions, Gibson (Gibson & Lanni, 1991) proposed a simple approach, based on the scalar diffraction theory and geometrical optics calculations. The aberration function is obtained through a calculation involving the ideal design parameters of the MO (cover slip refractive index, cover slip thickness, immersion oil refractive index) and their effective value. The simulations presented here were obtained by implementing the approach suggested by Haeberlé (2003), who combined the Gibson and the vectorial T6r6k models. Figure 5 summarizes the results of the simulations of the APSF of a x100 MO with 1.3 NA, with nonpolarized light, used under different conditions. If nonpolarized light is diffracted by the MO, the birefringence caused by the high NA MO would mix the cross-polarized components of the beam, while keeping a nonzero correlation among the cross-polarized components of the beam. Therefore, the cross-polarized components of the outgoing beam would cancel out for statistical reason, because the cross-polarized component of the emitted field would be uncorrelated. Therefore, the use of nonpolarized light ensures

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Correction for partial volume effects in PET: principle and validation

by Olivier Rousset

1998, Journal of nuclear medicine : official publication, Society of Nuclear Medicine

The accuracy of PET for measuring regional radiotracer concentrations in the human brain is limited by the finite resolution capability of the scanner and the resulting partial volume effects (PVEs). We designed a new algorithm to correct... more

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Comparison of aberrations in different types of progressive power lenses

by Pablo Artal

2004, Ophthalmic and Physiological Optics

Recently, computer numerically controlled machines have permitted the manufacture of progressive power lenses (PPLs) with different designs. However, the possible differences in optical performance among lens designs are not yet well... more

Figure 2. Measured zones in the PPLs with 4.0-mm in diameter.

Figure 5. Spatially resolved RMS for 4.0-mm pupil diameter, con- sidering defocus zero.

Figure 7. Average RMS of all tested zones of the lenses, for astigmatism and high order aberrations (coma and trefoil) with 4.0-mm pupil diameter. The error bars are the standard deviations. In the case of astigmatism, this parameter denotes how soft or hard the design is.

Figure 4. Zernike coefficients for the tested locations (for 4-mm diameter zones) of the three progressive lenses: in the corridor (yellow bars), 5 mm away from corridor (red bars for nasal zones and green bars for temporal zones) and 10 mm from corridor (dark red bars for nasal zones and dark green bars for temporal zones). Bars from left to right correspond to zones from far to near. The high order coefficients (from coefficient 6 to 12) are also shown on a larger scale. The Seidel aberrations corresponding to Zernike coefficients are noted on top of the figure.

Figure 6. (a) Contour plots of RMS considering only astigmatism, with 4.0-mm pupil size. (b) RMS for higher order aberrations, mainly coma and trefoil, because the other higher order aberrations are negligible.

Figure 8. Contour plots of addition for 4.0-mm pupil diameter. Figure 6 shows contour plots with iso-RMS lines for two different conditions: (1) only astigmatism and (2) only high order aberrations. The RMS for astigmatism in microns is related to astigmatism in diopters (C) by the following equation:

Figure 3. A modulus 2z representation of the WA maps and the associated PSFs, at three intermediate zones (C2 at the corridor, Nz and To at the nasal and temporal side), as examples of the twenty tested zones, for each PPL. (a) Considering defocus zero. (b) Considering defocus and astigmatism zero. 6.0-mm pupil diameter.

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Focusing on out-of-focus: assessing defocus estimation algorithms for the benefit of automated image masking

by Geert J Verhoeven

2018, ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences

Acquiring photographs as input for an image-based modelling pipeline is less trivial than often assumed. Photographs should be correctly exposed, cover the subject sufficiently from all possible angles, have the required spatial... more

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APPLICATION OF SHACK-HARTMANN WAVEFRONT SENSORS TO OPTICAL SYSTEM CALIBRATION AND ALIGNMENT

by Justin Mansell

1999, Adaptive Optics for Industry and Medicine

Optical systems are normally aligned by centering the energy distribution in various apertures. However, the use of both irradiance and phase information can in many cases greatly simplify this process, and can provide information for... more

Figure 2 - Simple graphical representation of average tilt, bear position, and beam size, and beam ellipticity.

Figure 3 - Aberrations for an F/5 lens rotated 15°. Note that the odd terms will results in a ne average tilt. Step 5 in the above list relies on an additional property of real optics. Consider the case of a doublet that is significantly rotated, as shown in Figure 3. In this case, numerous aberrations are introduced. The chief aberrations are astigmatism and defocus, although tilt, coma, spherical aberration and other terms may be present. However, if the initial irradiance distribution was centered on the SHWFS before inserting the lens, this position records accurately the average values. All of the

As an example of this process, this section presents the results of aligning and measuring the performance of a 24 inch diameter Cassegrain telescope at Stanford University. In this case, the SHWFS was mounted directly on the telescope with the addition of a single 50mm collimating lens. The SHWFS used was comparable in weight to the eyepieces used by the telescope, so did not appreciably affect the balance or weight load on the telescope. The process described above was used to align the system with a bright star (Arcturus) as a reference. Since this telescope operates almost at sea level, there was a significant amount of turbulence present during this process. Nevertheless, it was a straightforward matter to install, align and collimate the collimating lens and the wavefront sensor. Once installed, the sensor was used to record many images of different stars. Since the version of this sensor was not designed especially for low-light conditions, only a few bright stars were examined.

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Sensitivity to point-spread function parameters in medical ultrasound image deconvolution

by James Ng

2009, Ultrasonics

Clinical ultrasound images are often perceived as difficult to interpret due to image blurring and speckle inherent in the ultrasound imaging. But the image quality can be improved by deconvolution using an estimate of the point-spread... more

Clinical ultrasound images are often perceived as difficult to interpret due to image blurring and speckle inherent in the ultrasound imaging. But the image quality can be improved by deconvolution using an estimate of the point-spread function. However, it is difficult to obtain a sufficiently accurate estimate of the point-spread function in vivo because of the unknown properties of the soft tissue in clinical applications. Local variations in the speed of sound and attenuation change the pulse and beam shape. These in turn affect the point-spread function. The purpose and novelty of this paper is therefore to explore the sensitivity of a state-of-the-art deconvolution algorithm to uncertainty in the point-spread function. The point-spread function in our restoration algorithm is made shift invariant in the lateral dimension but shift dependent in the axial direction, and is modelled to match a 128-element 1D linear array often found in clinical use. We present simulated and in vitro sensitivity analyses of two-dimensional deconvolution while varying six parameters on which the point-spread function depends. Uncertainty in the ultrasound machine is analysed by varying the axial depths of lateral and elevational foci alongside height and width of transducer elements. Sensitivity to tissue influence is investigated by varying the speed of sound and frequency-dependent attenuation of the electro-mechanical impulse response. The results are analysed both quantitatively and in terms of the perceived image quality. First, the assessment of deconvolution using the logarithmic image amplitude is found to be a better indicator of the perceived improvement in the restoration. Secondly, the two most critical parameters for two-dimensional deconvolution are discovered to be the lateral focus and the speed of sound, because the success of deconvolution is perceived primarily in terms of deblurring. We also observed similar patterns for the simulation and in vitro experiment. Finally, we show that it is possible to restore in vivo ultrasound images using an assumed point-spread function and hence conclude that an exact point-spread function is not necessary for enhancing ultrasound image quality by deconvolution.

Fig. 14. Examples of deconvolved images and their mean correlation length for the in vitro phantom for various values of the speed of sound in soft tissue. The reference speed is 1540 m/s. For comparison purpose, the image has been re-scaled in the axial depth direction to the true dimensions of the designed phantom (that was scanned).

Fig. 8. Effect of the uniform variation in the frequency-dependent attenuation of the electro-mechanical impulse response in the ultrasound system: the PSF match vs. ISNR values and examples of deconvolved images.

Fig. 6. Effect of the variation in the width of the transducer elements on the PSF match and linear ISNR while the field-of-view and number of elements are fixed. The reference width is 170.8 um. The decibel values for the PSF match are shown on the left-hand side, and the linear version of the ISNR is shown on the right. The logarithmic version of the ISNR is not shown.

Fig. 4. Effect of the variation in the radius of the elevational focus: the PSF match vs. ISNR values and examples of deconvolution images. The reference focal radius is 13 mm.

Fig. 1. Diagram showing the key aspects of our deconvolution algorithm. The upper half shows the ultrasound image model (y=Hx+n) with our interpretation (x = Sw). The lower part is the algorithmic flow chart of the deconvolution itself. Notation: echogenicity (S), random component (w), reflectivity function (x), linear blurring operator (H), white Gaussian noise (n), and ultrasound image (y).

Fig. 5. Effect of the variation in the height of the transducer elements: the PSF match vs. ISNR values and examples of deconvolution images. The reference height is 6 mm.

Fig. 15. Examples of deconvolved images and their mean correlation length for the in vitro phantom assuming various degrees of frequency-dependent attenuation in the electro-mechanical impulse response.

Fig. 13. Examples of deconvolved images and their mean correlation length for the in vitro phantom for various values of the height of the transducer elements. The referenc height is 3.5 mm.

Fig. 11. Examples of deconvolved images and their mean correlation length for the in vitro phantom with the variation in the axial depth of the lateral focus. The reference focal depth is 16 mm. The dynamic range of the logarithmically compressed magnitude of the images is 80 dB. The title of each image shows its mean correlation length in the lateral direction, and those of the original ultrasound image and the reference deconvolution are 0.61 and 0.32 mm, respectively.

Fig. 2. Reference images for the simulation. (a) Reflectivity function or scatterer field, (b) blurred image with additive white Gaussian noise of SNR = 40 GB, (c) reference deconvolution of the image in (b), and (d) deconvolution of a noisy image blurred solely by Field II, which is not shown here. The dynamic range of the logarithmically compressed images is 80 dB. The probe surface corresponds to a value of zero in the axial depth dimension.

Fig. 12. Examples of deconvolved images and their mean correlation length for the in vitro phantom with varying values of the radius of the elevational focus. The reference focal radius is 9.6 mm.

Fig. 9. Reference images for in vitro phantom. (a) Image acquired by an ultrasound machine, (b) deconvolved image using the PSF with the reference parameters. The dynamic range of the logarithmically compressed magnitude of both images is 80 dB.

Fig. 7. Effect of the uniform variation in the speed of sound in soft tissue: the PSF match vs. ISNR values and examples of deconvolved images. The reference speed is 1540 m/s. For comparison purposes, the image has been re-scaled in the axial depth direction to the true dimensions of the simulated reflectivity function.

Fig. 3. Effect of the variation in the axial depth of the lateral focus: the PSF match vs. ISNR values and examples of deconvolved images. The reference focal depth is 16 mm. The dynamic range of the logarithmically compressed magnitude of the B-scan images is 80 dB. The title of each B-scan image shows two ISNR measures. The left value gives the linear version of the ISNR and the right value inside brackets gives the logarithmic version. The reference values are +12.04 and +5.81 dB, respectively. Images are chosen based on their logarithmic ISNR: plot (b) has a logarithmic ISNR of approximately 1.5 dB lower than that of the reference scenario, plot (c) is 3.0 dB lower, and plot (d) is 4.5 dB lower. The same convention is adopted in subsequent figures of simulation.

Fig. 10. Correlation length in the lateral direction of in vitro ultrasound images of a phantom in Fig. 9.

Fig. 16. Ultrasound images for in vivo forearm. (a) Image acquired by an ultrasound machine, (b) restored image using the PSF with the reference parameters. The dynamic range of the logarithmically compressed magnitude of the images is 80 dB.

Fig. 17. Correlation length in the lateral direction of in vivo ultrasound images of a forearm in Fig. 16.

Fig. 18. Example waveform of an electro-mechanical impulse response taken by ¢ General Electric RSP6-12 probe operated by Diasus ultrasound system from Dynamic Imaging Ltd.

Reference parameters for simulation. The wavelength is denoted by 2, which is based on the centre frequency and the speed of sound in the table. The specification is close to that of our clinical ultrasound system. The centre frequency was obtained from the Fourier Transform of the pulse in Fig. 18.

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A challenge problem for 2D/3D imaging of targets from a volumetric data set in an urban environment

by Curtis Casteel

2007, SPIE Proceedings

This paper describes a challenge problem whose scope is the 2D/3D imaging of stationary targets from a volumetric data set of X-band Synthetic Aperture Radar (SAR) data collected in an urban environment. The data for this problem was... more

Table 1. Calibration Array Data Descriptions The collected data for the challenge problem is stored in MATLAB binary format (*.mat files). Each file contains the phase history collected over one degree of azimuth for a single pass and a single polarization. With 8 passes and 4 polarizations per pass, the total number of files is 11,520 (360 * 8 * 4). The filenames are coded with the pass number, polarization, and azimuth angle. For example, file “data _3dsar_pass1_az001_HH.mat’ contains the data for all pulses from 0 to | degree azimuth from pass | operated at HH polarization. Loading a file gives a single MATLAB structure with fields containing the k-space data, frequencies, x,y,z-coordinate antenna locations, range to scene center, azimuth angle (degrees), and elevation angle (degrees). In addition, a simple autofocus solution is provided for the HH and VV polarizations.

Figure 5. 3-dimensional volumetric SAR image from the side view of the Ford Taurus Wagon using all eight passes with 360 degrees full aperture.

Figure 4. 3-dimensional volumetric SAR image from the front end view of the Ford Taurus Wagon using all eight passes with 360 degrees full aperture. Figure 3. Digital Picture reference of Ford Taurus Wagon used in the 3-dimensional SAR imaging of figures 4 and 5.

Figure 7. Layout diagram of the calibration array used in the spotlighted scene center.

Figure 2. Digital picture reference of parking lot consisting of vehicle staging center. All nine personal-owned-vehicles, case tractor and forklift displayed.

Figure 1. 2-dimensional SAR Image of the spotlighted scene center from a single pass with 360 degrees full aperture displays a spotlighted 2D SAR data image of the vehicle staging center and calibration target array from a single pass with 360 degrees full aperture. Figure 2 displays a digital picture of the targets assembled in the vehicle staging center. Upon comparison analysis of the vehicle staging center SAR image to the staging center digital image, two vehicles are missing due to scripted scenarios being orchestrated during the time period selected for the SAR image data to be processed. Figure | was selected only as a reference and example of imagery processed from the collected data.

Figure 6. Digital picture reference of the calibrated tophat reflector used in the calibration array of the spotlighted scene center.

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Assessing the optical performance of multifocal (diffractive) intraocular lenses

by Timo Eppig

2008, Ophthalmic and Physiological Optics

Background and purpose: While the optical performance of monofocal refractive lenses can be measured quite easily, more efforts are required to assess the performance of multifocal lenses, due to imaging to several foci. The purpose of... more

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Multistatic radar imaging of moving targets

by Margaret Cheney

2010, 2010 IEEE Radar Conference

We develop a linearized imaging theory that combines the spatial, temporal, and spectral aspects of scattered waves. We consider the case of fixed sensors and a general distribution of objects, each undergoing linear motion; thus the... more

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Volume Holographic Imaging in Transmission Geometry

by George Barbastathis

2004, Applied Optics

We address the performance of transmission geometry volume holograms as depth-selective imaging elements. We consider two simple implementations using holograms recorded with spherical and plane beams. We derive the point-spread function... more

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Image deblurring by means of defocus

by Andrew Stevenson

2004, Optics Communications

A new method for rapid deblurring (partial deconvolution) is proposed which is based on the physics of coherent image formation. The method uses slightly out-of-focus images in a way that makes the Fresnel diffraction counteract the... more

Fig. 3. Deblurred image obtained using Eq. (6) from noisy blurred image in Fig. 2.

Fig. 7. (a) Deblurred distribution of the projected thickness of Polyethylene obtained in accordance with Eq. (11); (b) cross-section of the deblurred thickness distribution through the edge of the sheet.

Fig. 2. Blurred image obtained by the convolution of the ‘ideal’ image from Fig. | with a 3x3 pixel wide Gaussian PSF and with 1% simulated Poisson noise.

Fig. 1. ‘Ideal’ 256x256 pixel image used in numerical experi- ments.

Fig. 5. (a) Experimental in-line X-ray image of an edge of a Polyethylene sheet; (b) cross-section of image intensity through the edge o: the sheet.

Fig. 6. (a) Distribution of the projected thickness of Polyethylene reconstructed according to Eq. (10); (b) cross-section of the reconstructed thickness distribution through the edge of the sheet.

Fig. 4. Deblurred image obtained using Eq. (12), i.e. the noisy blurred defocused image at the optimal defocus distance 29".

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Breaking the resolution limit in light microscopy

by Rainer Heintzmann

2006, Briefings in functional genomics & proteomics

Fluorescent imaging microscopy has been an essential tool for biologists over many years, especially after the discovery of the green fluorescent protein and the possibility of tagging virtually every protein with it. In recent years... more

Figure 4: Linear structured illumination of Drosophila Polytene chromosomes stained with Sytox Green (a) Widefield image obtained by summing all the individual images under structured illumination. (b) Reconstruction of the sample from the structured illumination data (5 phases, 2 angles).

WF, widefield; CLSM, confocal laser scanning microscopy; LSM, laser scanning microscopy; 4Pi, stands for the full solid angle of a sphere; 15M, incoherent interference illumination microscopy image interference microscopy; PALM, photoactivated localization microscopy; STORM, stochastic optical reconstruction microscopy; SIM, structured illumination microscopy; PEM, patterned excitation microscopy; LMEM, laterally modulated excitation microscopy; HELM, harmonic excitation microscopy; SPEM, saturated patterned excitation microscopy; SSIM, saturated structured illumination microscopy; 2P, two photon; STED, stimulated emission depletion; TIRFM, total internal reflection microscopy; SNOM, NSOM, scanning near field optical microscopy. Table I: Fluorescence Microscopy Methods

Figure I: The Point Spread Function (PSF). Two PSFs are shown, one for high numerical aperture (NA = 1.3 in grey) and one for NA=0.3 (slightly transparent shades). As can be seen the low NA PSF is wide and has well-defined positions of zero intensity, leading to the definition of the Rayleigh limit. For this PSF also the definition of full width measured at half the maximum (FWHM) is shown. The high NA PSF (uniformly grey peak in the middle) is much finer, but does not have the rings of zero intensity. The colour version of this figure can be found in www.bfgp.oxfordjournals.org

Figure 2: The Abbe limit (a) Diffraction of a parallel light beam from a periodic grating structure (only the zero and first diffraction order are shown) (b) Diffracted light from a fine periodical structure already fails to fall within the angular acceptance range of the objective lens. The image can thus only be formed from the undiffracted zero order yielding a flat image of equal intensity. (c) For fluorescence the emitters have to be considered independently and intensity will be added. Nevertheless, the finest resolution (constituent of the PSF) is still defined by the biggest angle of emitted light rays that were captured and refocused. The colour version of this figure can be found in www.bfgp.oxfordjournals.org

Figure 3: Confocal and 4Pi Image. Comparison of volume rendered images of the actin cytoskeleton and the nucleus of muscle support The nucleus was stained wit tissue endothelial cells. h DAPI and the actin cytoskeleton with Alexa488-phalloidin. (a) 2-photon confocal view of the sample (b view (after 3-point deconvo The improved resolution and biological structures is visible. T 2-photon 4Pi (type A) ution) of the sample. better discrimination of his data set corresponds to a width of 234 11m, a height of 2.9,1m and a depth of 30.01m. Sample prepared by Elisabeth Ehler. The colour version of this figure can be found in www.bfgp.oxfordjournals.org

Figure 5: Stimulated emission depletion image. Revealing the nanopattern of the SNARE protein SNAP-25 on the plasma membrane of a mammalian cell. Confocal (a) vs. STED image (b) of the antibody-tagged proteins. The encircled areas show linearly deconvolved data. STED microscopy provides a substantial leap forward in the imaging of protein self-assembly; here it reveals for the first time that SNAP-25 is ordered in clusters of «60 nm average size. (reproduced with permission of the Institute of Physics from reference 39). The colour version of this figure can be found in www.bfgp.oxfordjournals.org

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Imaging moving targets from scattered waves

by Margaret Cheney

2008, Inverse Problems

We develop a linearized imaging theory that combines the spatial, temporal and spectral aspects of scattered waves. We consider the case of fixed sensors and a general distribution of objects, each undergoing linear motion; thus the... more

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<title>Imaging that exploits spatial, temporal, and spectral aspects of far-field radar data</title>

by Margaret Cheney

2008, Algorithms for Synthetic Aperture Radar Imagery XV

We develop a linearized imaging theory that combines the spatial, temporal, and spectral aspects of scattered waves. We consider the case of fixed sensors and a general distribution of objects, each undergoing linear motion; thus the... more

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3D Microscopy Deconvolution using Richardson-Lucy Algorithm with Total Variation Regularization

by Josiane Zerubia

2004

Confocal laser scanning microscopy is a powerful and increasingly popular technique for 3D imaging of biological specimens. However the acquired images are degraded by blur from out-of-focus light and Poisson noise due to photon-limited... more

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Multiscale geostatistical analysis of AVHRR, SPOT-VGT, and MODIS global NDVI products

by Molly Brown

2008, Remote Sensing of Environment

Global NDVI data are routinely derived from the AVHRR, SPOT-VGT, and MODIS/Terra earth observation records for a range of applications from terrestrial vegetation monitoring to climate change modeling. This has led to a substantial... more

Global NDVI data are routinely derived from the AVHRR, SPOT-VGT, and MODIS/Terra earth observation records for a range of applications from terrestrial vegetation monitoring to climate change modeling. This has led to a substantial interest in the harmonization of multisensor records. Most evaluations of the internal consistency and continuity of global multisensor NDVI products have focused on time-series harmonization in the spectral domain, often neglecting the spatial domain. We fill this void by applying variogram modeling (a) to evaluate the differences in spatial variability between 8-km AVHRR, 1-km SPOT-VGT, and 1-km, 500-m, and 250-m MODIS NDVI products over eight EOS (Earth Observing System) validation sites, and (b) to characterize the decay of spatial variability as a function of pixel size (i.e. data regularization) for spatially aggregated Landsat ETM+ NDVI products and a real multisensor dataset. First, we demonstrate that the conjunctive analysis of two variogram properties -the sill and the mean length scale metric -provides a robust assessment of the differences in spatial variability between multiscale NDVI products that are due to spatial (nominal pixel size, point spread function, and view angle) and non-spatial (sensor calibration, cloud clearing, atmospheric corrections, and length of multi-day compositing period) factors. Next, we show that as the nominal pixel size increases, the decay of spatial information content follows a logarithmic relationship with stronger fit value for the spatially aggregated NDVI products (R 2 = 0.9321) than for the native-resolution AVHRR, SPOT-VGT, and MODIS NDVI products (R 2 = 0.5064). This relationship serves as a reference for evaluation of the differences in spatial variability and length scales in multiscale datasets at native or aggregated spatial resolutions. The outcomes of this study suggest that multisensor NDVI records cannot be integrated into a long-term data record without proper consideration of all factors affecting their spatial consistency. Hence, we propose an approach for selecting the spatial resolution, at which differences in spatial variability between NDVI products from multiple sensors are minimized. This approach provides practical guidance for the harmonization of long-term multisensor datasets.

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Relative focus map estimation using blind deconvolution

by Tamás Szirányi

2005, Optics letters

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Image restoration of skin scattering and optical blurring for finger vein recognition

by Vanitha Ramalingam

2011, Optics and Lasers in Engineering

Finger vein recognition has been adopted due to its high recognition rate and the invisibility of vein in visible light. However, because a finger vein pattern is not distinctive due to light scattering in the skin layer, the localization... more

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Video Stabilization Performance Assessment

by Marius Tico

2006, 2006 IEEE International Conference on Multimedia and Expo

Taking videos with a hand-held camera introduces shaking, which incontrovertibly reduces video quality. Digital video stabilization is a process to compensate for camera motion by means of image processing. In the best case, it does not... more

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An image super-resolution algorithm for different error levels per frame

by hu he

2006, IEEE Transactions on Image Processing

In this paper, we propose an image super-resolution (resolution enhancement) algorithm that takes into account inaccurate estimates of the registration parameters and the point spread function. These inaccurate estimates, along with the... more

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Disparity-Based Space-Variant Image Deblurring

by Changsoo Je

2013

Obtaining a good-quality image requires exposure to light for an appropriate amount of time. If there is camera or object motion during the exposure time, the image is blurred. To remove the blur, some recent image deblurring methods... more

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Depth of field postprocessing for layered scenes using constant-time rectangle spreading

by Michael Tao and

2009

Control over what is in focus and what is not in focus in an image is an important artistic tool. The range of depth in a 3D scene that is imaged in sufficient focus through an optics system, such as a camera lens, is called depth of... more

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Water proton T1 measurements in brain tissue at 7, 3, and 1.5 T using IR-EPI, IR-TSE, and MPRAGE: results and optimization

by ST FRANCIS

2008, Magma (New York, N.Y.)

This paper presents methods of measuring the longitudinal relaxation time using inversion recovery turbo spin echo (IR-TSE) and magnetization-prepared rapid gradient echo (MPRAGE) sequences, comparing and optimizing these sequences,... more

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The impact of gridding artifacts on the local spatial properties of MODIS data: Implications for validation, compositing, and band-to-band registration across resolutions

by Bin Tan

2006, Remote Sensing of Environment

Gridding artifacts between observations and predefined grid cells strongly influence the local spatial properties of MODIS images. The sensor observation in any grid cell is only partially derived from the location of the cell, with the... more

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Imaging with multi-aperture optical telescopes and an application

by Laurent Mugnier

2001, Comptes Rendus de l'Académie des Sciences - Series IV - Physics

The two main types of Multi-Aperture Optical Telescopes (MAOTs) (so-called Michelson and Fizeau) and the two possible modes of optical beam combination are reviewed. Widefield imaging with a Michelson instrument is studied and the... more

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Quantitative Techniques for PET/CT: A Clinical Assessment of the Impact of PSF and TOF

by Joshua Schaefferkoetter

2013

Figure 21. LROC curve from the distributions in Figure 2(

Figure 17. The circular geometry of PET scanners introduces registration errors for photons striking the detectors at highly oblique angles, blurring the system point interaction effects within the crystal block and event misregistration.

Figure 23. A random Gaussian process and the respective histogrammed density statistic.

Figure 42. Comparison of physician performance in localization of liver and lung lesions

Figure 39. Templates of the 8 numerical observers evaluated in this study (blue) filter).

Figure 14. Filtered backprojection process

Figure 7. The detector elements in a system with span 7 only accept coincident cross plane calculations. The case for span 7 is illustrated below in Figure 7. he span was 3, i.e. 0, which refers to the direct planes, and +/- 1, which contribute to the

Figure 12. Raw sinogram (left) and the same sinogram corrected for attenuation, randoms, scatter, and normalization.

Figure 6. Diagram showing the 3 types of prompt detections: scatter, random, and true.

Other derivatives of the ROC model include free-response receiver operating

Figure 20. Probability distributions for the LROC model

Figure 22. Cumulative and probability density functions, along with the resultin:

Figure 40. Performances of 3 physician observers in the detection and

Figure 8. Representation of the different segments acquired in 3D acquisition. elements where the difference is greater than or equal to 11.

determined for a human observer, without knowledge of the specific test statistics.

is Py and P,, respectively. This model yields a direct calculation of localization accuracy approach defines the likelihood function given by

Figure 10. Attenuation reduces information about internal structure; the image

Figure 16. Time of flight information reduces the noise in the reconstruction and photon timing measurements became possible in clinical PET.

Figure 25. The distribution covariance is used with the mean difference to define the optimal discriminant function in correlated noise.

Table 2. Comparison of different PET scintillators and their properties "A routine whole-body scan (from the cranial orbits to mid-thigh) typically includes 4-6 bed positions. Melanome scans of the entire body use as many as twelve. an array of 13 x 13 LSO crystals (Jakoby, Bercier et al. 2008).

Figure 4. Transaxial PET, CT, and fused images of a 40 year-old female with a

Table 1. Examples of commonly used isotopes used for PET These isotopes are formed in a cyclotron, where a high energy proton beam substitution. Table 1 lists the properties of some commonly used isotopes.

Figure 34. In the CHO model, the class means and intraclass scatter matrices

Figure 33. In the CNPW model, the class means define the discriminant function

qualitative comparison of the four reconstructions is seen in Figure 37.

Figure 36. Plots of observer SNR; maximum SNR defined the optimal processing parameters Based on the observer results, the reconstruction parameters were chosen as

Figure 35. The new CHO discriminant function resulting from observer noise

Figure 29. Channel profiles for the S-DOG configuration and Barrett 2001), the channel profiles are seen in Figure 29.

Figure 47 shows the gain in observer performance for patients with low and high TOF showed more improvement than PSF. For all iterations of each respective Discussion

Figure 45. LROC curves showing mean localization performance of liver lesions of human and mathematical observers in the localization task of lesions in the liver. than the whitening operation.

Figure 15. Expectation maximization (right) is less sensitive to noise relative to backprojection, both reconstructions being of the same projection data.

still have enough energy to be accepted. Thus, many scattered events are not rejected by Scatter is an important problem in 3D PET, as in aclinical scan, 30-50% of the LSO-based scanners). However, a photon can scatter through a relatively large angle and data may be from scattered photon events (Cherry, Dahlbom et al. 1991).

figures below illustrate the improved diagnostic capacity of fused images. information as well as anatomical location. The disease is not obvious in the CT image alone but the PET scan shows an intense focus of metabolic activity medial to the hepatic

Figure 11. Bilinear scaling function used to convert CT numbers (HUs) to linear tissue, and above 80 as bone tissue. The CT-to-PET ACF scaling is 2.26 and 1.90 > Houndsfield units are used in X-ray CT to represent the electron density of biological tissue. The values are calibrated so that water is zero, with more and less dense material lying in the positive and negative ranges, respectively.

Figure 2. Shipments of PET and PET/CT scanners for the US markets as recorded half being that of dedicated PET scanners. By 2005, PET/CT systems had almost The first PET scans were conducted in the 70’s at Washington University in St.

Figure 5. Positron emission and annihilation. Within the atomic nucleus, a proton on the initial positron energy as well as surrounding tissue. electron. The mean free path of a positron in water is 0.6mm, but the actual path depends a positron which then encounters a nearby electron, and the pair self-annihilate,

Figure 38. The viewer program developed to present the images and record a 5-point scale by which to rate the confidence in their decision. decision data

method Table 4. Distributions of mean lesion contrasts, grouped by reconstruction To generate a large population of test images, the lesion strength and scaling

Figure 27. The process of simulating realistic lesions in patient scans. the patient CT data. The attenuated lesion sinogram was then added to that of the patient.

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Monolithic scintillator PET detectors with intrinsic depth-of-interaction correction

by Freek Beekman

2009, Physics in Medicine and Biology

We developed positron emission tomography (PET) detectors based on monolithic scintillation crystals and position-sensitive light sensors. Intrinsic depth-of-interaction (DOI) correction is achieved by deriving the entry points of... more

Table 2. FWHM and FWTM of the cross-sections in the x- and y-directions of the measured (PSF,) and corrected (PSF) point-spread functions of crystal RO1-P at the detector centre and at normal incidence. These results were obtained at room temperature with L = 500 and Ey, ~ 100 keV.

Figure 3. Schematic representation of the setup used for the experimental characterization of the detectors.

Figure 5. Pulse-height spectrum of detector RO1-P measured at 511 keV (dots). A Gaussian fit tc the full-energy peak is also shown (solid curve).

Figure 7. Measured point-spread function PSF,(x, y) of crystal RO1-P at the detector centre, obtained at normal incidence using L = 500. The result is not yet corrected for the beam diameter dp = 0.96 mm FWHM.

Figure 2. Average APD gains of each 2 x 8 pixel bank of the Hamamatsu S8550SPL arrays (serial numbers 036 and 037) as a function of AV (see equation (1)), measured with 5.89 keV x-ray photons directly incident on the APDs.

Figure 6. Timing spectrum measured with crystal RO1-P against a BaF2-PMT detector (dots). A Gaussian fit through the data is also shown (solid curve).

Table 1. Absolute light yield of the crystals investigated, and corresponding energy resolutions measured with a 7*Na source (511 keV). The 2c-uncertainties are ~10% for the light yields and ~0.2% FWHM for the energy resolutions.

Figure 10. FWHM and FWTM of 1D-PSF,(x’) and 1D-PSF,(y’) of crystal T02-P, averaged over the entire crystal length and projected onto a plane perpendicular to the test beam, as a function of the angle of incidence 6 at (a) y = 0° and (b) g = 90°. Results are not corrected for dy = 0.96 mm FWHM. The estimated uncertainty is ~0.05 mm for the FWHM and ~0.2 mm for the FWTM (20).

Table 3. FWHM and FWTM of uncorrected 1D point-spread functions, measured along the x- and y-axis of several trapezoidal and rectangular detectors and averaged over the entire crystal length. Results are not corrected for dy) = 0.85 mm FWHM. The value of L that minimized the FWHM (typically, 100 < L < 1000) was used in all cases. The estimated uncertainty is ~0.05 mm for the FWHM and ~0.2 mm for the FWTM (20).

Figure 8. FWHM of PSF,(x) of crystal RO1-P measured at normal incidence as a function of the test beam position, using L = 500. Values are derived from 2D error histograms averaged over 1 x 1 mm? segments and are not corrected for dy = 0.96 mm FWHM.

Figure 4. Schematic representation of the readout electronics. Components are denoted by CSP: charge-sensitive preamplifier; SA: shaping amplifier; MC-ADC: multichannel ADC; ©: summing amplifier; TFA: timing filter amplifier; CFD: constant-fraction discriminator; CC: coincidence circuit.

Figure 9. Measured (closed circles) and modelled (dotted curve) uncorrected PSF cross-sections PSF,(x), and cross-section PSF(x) of the corrected PSF (solid curve), derived from the measured PSF,(x, y) at the centre of crystal RO1-P shown in figure 7.

Figure 1. Schematic representation of the trapezoidal (a) and rectangular (b) detector geometries with double-sided APD array readout. In both drawings, the arrow indicates the path of ar annihilation photon incident on the front surface of the detector. The coordinate system used tc specify the entry point and angle of incidence is also indicated. Dimensions are in mm.

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Reducing the dispersion error in the digital waveguide mesh using interpolation and frequency-warping techniques

by Vesa Välimäki

2000, IEEE Transactions on Speech and Audio Processing

The digital waveguide mesh is an extension of the onedimensional (1-D) digital waveguide technique. The mesh can be used for simulation of two-and three-dimensional (3-D) wave propagation in musical instruments and acoustic spaces. The... more

Fig. 2. Dispersion factor in the 2-D rectangular digital waveguide mesh. The distance from the center is directly proportional to the frequency, and the ratio of 1 and €2 (with the sign) determines the propagation direction. In (a), the value 1 represents the ideal speed which is achieved in diagonal directions at all frequencies, but in all other directions there is dispersion except at dc. The equal dispersion factor contours in (b) descend from the center point in increments of 1%. represents the wave propagation speed in the directio1 a = arctan(€2/é,). The difference scheme (2) is lossless since l9(é1,&)| = V/A/4)b(Er, €2)? + 1/4)[4 — (21, &2)?] = 1 as shown in [3]. The wave propagation speed of the scheme can now be calculated from the equation

Fig. 4. Dispersion factor in the triangular digital waveguide mesh. gets a new formulation which includes the linear-phase tern associated with the six junction points [8]:

Fig. 8. Bilinear interpolation coefficients are calculated from this geometry.

Fig. 9. The allpass-filter structure which is used in the warping of a simulation result of the interpolated waveguide mesh. A)/(1 + Az7+), as illustrated in Fig. 9. The extent of warping is determined by the allpass filter coefficient \, which is the same for all the allpasses in the chain. Tap coefficients are set equal to the signal samples s(n) to be warped. The signal to be warped can be picked up at any position (2, y) on the mesh such that s(n) = p(n, x,y). When a unit impulse is fed into this filter structure, the output signal s,,,(7) is the frequency- warped version of the original signal [26]-[28].

Fig. 1. In the original 2-D digital waveguide mesh each scattering junction J is connected to four neighbors with unit delays. where w, = 27&1,w2 = 2n€2, and & and & are normalized spatial frequencies

Fig.5. The construction phases of the interpolated 2-D digital waveguide mesh structure: (a) the original mesh with four directions, (b) the hypothetical version with H propagation directions, (c) the case H = 8 for which the best results have been obtained, and (d) the new interpolated waveguide mesh, in which the new nodes are spread onto the neighboring nodes by deinterpolation.

Fig. 7. Maximal and minimal relative frequency errors represented by solid and dotted lines for the (a) rectangular, (b) triangular, (c) hypothetical eight-directional, (d) first-order Lagrange interpolated, (e) second-order Lagrange interpolated, and (f) optimally interpolated digital waveguide mesh structures as a function of normalized frequency, where 0.5 corresponds to the Nyquist limit. Note that in the original rectangular structure there is no error in the diagonal direction.

Fig. 6. The dispersion factor in the following digital waveguide mesh structures: (a) hypothetical eight-directional, (b) bilinearly interpolated eight-directional (c) second-order Lagrange interpolated eight-directional, and (d) optimized interpolated mesh. The equal dispersion factor contours descend from the center poin in increments of 1%.

eo For the eight-directional mesh, the coefficients are ha = 1/2,hg = V2, andh, = 6-4/2 = 0.343146. These coefficients satisfy the stability condition (21) with the 2quality sign, and the structure is thus lossless. Figure 6(b) shows the wave travel speed in the bilinearly interpolated sight-directional structure. Maximal and minimal RFE’s obtained by this structure are presented in 7(d). Comparison of Fig. 6(a) and (b) shows that the bilinearly interpolated mesh jives a relatively good approximation of the eight-directional mesh. One disadvantage of this structure is that the dispersion factor at low frequencies is Using these interpolation coefficients, the weighting coeffi- cients for an H-directional mesh are

Fig. 13. Relative frequency errors obtained from the square membrane simulations with the original rectangular (squares), warped interpolated (hexagrams), and warped triangular (triangles) digital waveguide mesh structures. Each mark in the figure corresponds to one eigenmode of the membrane.

Fig. 11. Maximal and minimal relative frequency errors represented by solid and dashed lines in the (a) rectangular, (b) warped interpolated (A = —0.327358), and (c) warped triangular (A = —0.109540) digital waveguide mesh structures. The warping coefficients were optimized to minimize the maximal error. Note the different scale in (a).

Fig. 3. The triangular digital waveguide mesh structure. (Qmaxrect = 2(€1,€2) = ka /2, where k = 0,1, 2, or 3). The response of the rectangular digital waveguide mesh begins to repeat at normalized temporal frequency 0.25, and that is repre- sented by an emphasized circle in Fig. 2(b) [4], [7].

Fig. 12. Eigenfrequencies of an ideal square membrane, which is clamped on each boundary, simulated using the (a) rectangular, (b) warped interpolated (A = —0.327358), and (c) warped triangular (A = —0.109540) digital waveguide mesh. The analytic solution for the magnitude response is shown by the dashed line.

Fig. 10. There are two alternative techniques how the warped digital waveguide mesh can be used. Both techniques apply frequency warping to input and output signals of the waveguide mesh, and in the first technique (a) the spatial sampling grid is resampled and in the second one (b) the input and output signals are frequency scaled.

COMPUTATIONAL REQUIREMENTS OF VARIOUS MESH STRUCTURES filter. The length of the output signal of the filter has to be longer than £. Thus the computational cost of warping depends only on the length of the warped signal and not on the size of the mesh.

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Volumetric ultrasound imaging using 2-D CMUT arrays

by Butrus Khuri-Yakub and

2003, Ultrasonics, …

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 50, NO. 11, NOVEMBER 2003

Fig. 4. Schematic view of the 8 x 16 2-D array showing the transmit and receive apertures and the coordinate axes. Fig. 3. Experimental setup with 3-D imaging phantoms.

ORALKAN et al.: VOLUMETRIC ULTRASOUND IMAGING USING 2-D CMUT ARRAYS Fig. 1. 2-D CMUT array. {a) Schematic cross section of a CMUT cell. (b) 3-D model of a CMUT cell with a through-wafer via interconnect. (c) Top view of a through-wafer via. (d) SEM cross section of a through-wafer via. (e) Top view of multiple 2D CMUT elements forming an array. (f) Top view of a single 2-D CMUT array elernent. (g) Top view of individual CMUT cells constituting 2-D array elements.

ORALKAN et al.:; VOLUMETRIC ULTRASOUND IMAGING USING 2-D CMUT ARRAYS Fig. 13. Grayscale images of the spherical target at a constant range with a display dynamic range of 40 dB. (a) Experiment. (b) Hemispherical reflector model (experimental equivalent). (c) Point reflector model. (d) Point reflector model when full 8 x 16 aperture used for receive.

PuysicaL PARAMETERS OF THE 2-D CMUT ARRAY. TABLE I device capacitance is very small. To integrate 2-D trans- ducer arrays with associated transmit/receive electronics, as briefly discussed in Section J, several different inter- connection schemes have been proposed in the literature. Monolithic integration of CMUTs with electronic circuits has also been proposed [35]-[38]. Monolithic integration of microelectromechanical systems (MEMS) with electronic circuits usually results in a compromise of the perfor- mance of one or both components. It has been demon- strated that a modified CMOS or BiCMOS process could

IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL, VOL. 50, NO. 11, NOVEMBER 2003 Fig. 11. Cross-sectional images of the spherical phantom. (a) Azimuthal grayscale cross-sectional image with a display dynamic range of 20 dB. {b) Azimuthal grayscale cross-sectional image with a display dynamic range of 40 dB. (c} Elevational grayscale cross-sectional image with a display dynamic range of 20 dB. (d) Elevational grayscale cross-sectional image with a display dynamic range of 40 dB.

Fig. 7. 3-D coordinate system used for image reconstruction.

Fig. 2. 2-D array assembly. (a) 32 x 64 2-D CMUT array diced from a 128 x 128-element array. (b) Schematic representation of 3-D multichip assembly. (c) Top view of the glass carrier chip layout to fan out a 16 x 16 portion of the 2-D CMUT array. (d} The printed circuit board (PCB) carrying the flip-chip-bonded 2-D array-glass substrate assembly. (e) Magnified view of the center portion of the PCB showing the wire bonds from glass substrate to the PCB. ORALKAN et ail.: VOLUMETRIC ULTRASOUND IMAGING USING 2-D CMUT ARRAYS

Fig. 8. Reconstructed 3-D image of the parallel plate phantom. (a) Elevational grayscale cross-sectional image with a display dynamic range of 40 dB. (b) Surface-rendered 3-D image superimposed on the parallel plate phantom model. (c) Azimuthal grayscale cross-section image with a display dynamic range of 40 dB.

Fig. 5. (a) Measured echo signal from the top surface of the plate phantom. (b) Corresponding frequency spectrum. ORALKAN et al.: VOLUMETRIC ULTRASOUND IMAGING USING 2-D CMUT ARRAYS Fig. 6. (a) Measured echo signal from the spherical phantom. (b) Cor- responding frequency spectrum.

Fig. 14. (a) Azimuthal cross section of the constant range images. {b) Elevational cross section of the constant range image.

Fig. 12. (a) Simulated echo signal from the spherical phantom. (b) Corresponding frequency spectrum.

Fig. 9. Top view of the reconstructed 3-D image of the parallel plate phantom. Fig. 10. Surface-rendered 3-D image of the spherical phantom.

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Measurement of the point spread function in MRI using constant time imaging

by Todd Constable

1997, Magnetic Resonance in Medicine

The point spread function is a fundamental property of magnetic resonance imaging methods that affects image quality and spatial resolution. The point spread function is difficult to measure precisely in magnetic resonance even with the... more

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A visual odometry framework robust to motion blur

by Emanuele Menegatti

2009, 2009 IEEE International Conference on Robotics and Automation

Motion blur is a severe problem in images grabbed by legged robots and, in particular, by small humanoid robots. Standard feature extraction and tracking approaches typically fail when applied to sequences of images strongly affected by... more

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Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement

by Peyman Milanfar

2001, IEEE Transactions on Image Processing

In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters... more

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Odd aberrations and double-pass measurements of retinal image quality

by Pablo Artal

1995, Journal of the Optical Society of America A

We investigated the formation of the aerial image in the double-pass method to measure the optical quality of the human eye. We show theoretically and empirically that the double pass through the eye's optics forces the light distribution... more

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Point-spread function retrieval for fluorescence microscopy

by Praveen Pankajakshan

2009, … Imaging: From Nano …

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Blur identification by multilayer neural network based on multivalued neurons

by Igor Aizenberg

2008, Neural Networks, IEEE …

It is worth to note that the factor 1/(n + 1) in (3) is an im- portant constant part of the learning rate. The use of this factor ensures distribution of the error among all the neuron’s inputs. Because all of them are equitable, it is natural to consider that the error is uniformly distributed among all the n + 1 synaptic weights. Without this factor the weighted sum would be changed by d6(n + 1) instead of 6. This would lead to the permanent jumping over the desired output, without the convergence of the learning algorithm [2], [6]. of weights according to (3) changes the weighted sum exactly by the value 6, so by the value of the error

Fig. 5. Structure of the feedforward neural network used for both blur model and its parameter identification.

Fig. 3. Types of PSF used: (a) Gaussian PSF with t = 2 and size 21 x 21; (b) linear uniform motion blur of the length 5; (c) boxcar blur of the size 3 x 3; (d) frequency characteristics of (a); (e) frequency characteristics of (b); (f) frequency characteristics of (c).

Fig. 2. Geometrical interpretation of the MVN learning rule.

Fig. 6. Structure of the neural element on the output layer of MLMVN.

Fig. 7. (a) Test noisy blurred Cameraman image with Gaussian PSF tT = 2 (b) reconstructed using the regularization technique [18] after the blur and its parameter has been identified as Gaussian PSF with r = 2 (ISNR = 3.88 dB): (c) the original Cameraman image blurred by the Gaussian PSF with T = 1.835 [this blurred image does not differ visually from the one in Fig. 7(a)] and then reconstructed using the regularization technique [18] after the blur and its pa- rameter has been identified as Gaussian PSF with r = 2 (ISNR = 3.20 dB): (d) the original Cameraman image blurred by Gaussian PSF with 7 = 2.165 [this blurred image does not differ visually from the one in Fig. 7(a)] and then reconstructed using the regularization technique [18] after the blur and its pa- rameter has been identified as Gaussian PSF with r = 2 (ISNR = 3.22 dB).

Fig. 1. Geometrical interpretation of the MVN activation function. The structure of this paper is as follows. In Section II, we in- troduce MVN and MLMVN and their training algorithms. The problem of image deconvolution is described in Section II]. The use of MLMVN for blur identification is described in Section IV, and simulation results are presented in Section V. The exact derivation of the error backpropagation algorithm for the MLMVN is presented in Appendix I. Numerical ex- ample that illustrates training of the MLMVN is presented in Appendix II.

Fig. 4. True test Cameraman image (a) blurred by (b) Gaussian blur with t = 2; (c) boxcar blur of the size 9 x 9 log |Z| of the true test Cameraman image (d) blurred by (e) Gaussian blur with tr = 2; (f) rectangular blur of the size 9 x 9. The normalized log | Z| values used as arguments to generate training vectors in (26) and (27) obtained from the true test Cameraman image (g) blurred by (h) Gaussian blur with t = 2; i) boxcar blur of the size 9 x 9.

*The Training Error (column “Train. Er.”) is provided only for Fletcher- Reeves Conjugate Gradient technique since all others are trained till 0 error. COMPARISON OF SPEED OF CONVERGENCE (ITER.) AND CLASSIFICATION RATES (CR) FOR GAUSSIAN BLUR PARAMETER IDENTIFICATION TABLE I

*Experiment 1 and Experiment 2 are not comparable to each other because they simulate the different problems (see Section V.B) CR FOR BLUR IDENTIFICATION

COMPARISON OF SPEED OF CONVERGENCE (ITER.) AND CLASSIFICATION RATES (CR) FOR GAUSSIAN BLUR PARAMETER IDENTIFICATION OF A STANDARD REAL-VALUED MLF WITH EXTENDED TOPOLOGY 10 — 71 — 1 (5+1)+6- (35+ 1) = 2336 weights in total. Because the standard MLF shows significantly worse results in comparison to the MLMVN for a simpler problem in Section V-A (Table I), we do not provide here results for the multiple-blur identifica- tion with MLF.

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<title>Laser dazzling of focal plane array cameras</title>

by Frank van Putten and

2007, Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XVIII

Figure 1. Impact of increasing laser irradiance on the InSb camera image. Laser dazzling of infrared focal olane array cameras

Figure 2. Observed laser dazzle image in the InSb camera, for maximum-power, short-pulse laser irradiance. Figure 3. Imaging seeker simulator including the CMT camera.

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An Anatomically Realistic Simulation Framework for 3D Ultrasound Localization Microscopy

by Hatim Belgharbi

IEEE Open Journal of Ultrasonics, Ferroelectrics, and Frequency Control

The resolution of 3D Ultrasound Localization Microscopy (ULM) is determined by acquisition parameters such as frequency and transducer geometry but also by microbubble (MB) concentration, which is linked to the total acquisition time... more

FREDERIC LESAGE received the B.Sc. degree in physics from Laval University, Canada, in 1991, the Diploma degree in applied mathe- matics and theoretical physics (advanced study) from Cambridge University, U.K., in 1992, and the Ph.D. degree in physics from Université Paris-Sud/Saclay in 1995. Following postdoctoral fellowships, he worked in the private sector with d Y Lockheed-Martin Canada and ART Advanced Technologies. He is currently a Full Professor with the Department of Electrical Engineering, Polytechnique Montréal. He also holds the Canada Research Chair of Vascular Optical Imaging. His current research interests include non-linear optical microscopy applied to vascular diseases. LEO MILECKI (Graduate Student Member, IEEE) received the B.Sc. degree from CentraleSupélec, Paris-Saclay University, France, in 2019, focusing on applied mathematics and data science, where he is currently pursuing the Ph.D. degree. During which, he interned at the Provost Ultrasound Laboratory, Polytechnique Montréal, where he successfully designed a deep learning framework for ultrasound localization microscopy. He also studies the application of novel machine learning algorithms to analyze biomedical data toward graft rejection diag- nostic or prognosis after renal transplantation, focusing on deep learning and un-/weakly-/self-supervised methods. “ His research interests include clinically translatable ultrasound localization microscopy. HATIM BELGHARBI (Member, IEEE) received the B.Ing. and M.Sc.A. degrees in biomedi- cal engineering from Polytechnique Montréal, Montreal, Canada, in 2019 and 2021, respectively. He is currently pursuing the dual Ph.D. degree with the Joint Department of Biomedical Engi- neering, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA, and NC State Univer- sity, Raleigh, NC, USA. He is also a member of Paul Dayton and Gianmarco Pinton Laboratories. His research interests include clinically translatable ultrasound localization microscopy. RAFAT DAMSEH received the B.S. degree in telecommunication engineering from Yarmouk University, Irbid, Jordan, in 2011, the M.Sc. degree in electrical and computer engineering from Concordia University, Montreal, Canada, in 2015, and the Ph.D. degree in biomedical engi- neering from Polytechnique Montréal, Montreal, in 2020. He did postdoctoral research at the Harvard Medical School, Boston, MA, USA, from 2020 to 2021. He is currently an Assistant Professor with the Department of Computer Science and Software Engineer- ing, United Arab Emirates University, Al-Ain, United Arab Emirates. His research interests include medical image computing and reconstruction and computational neuroimaging.

FIGURE 1. Simulation framework. All sub-figures are scaled to match the same scalebar. (A) Two-photon microscopy (2PM) of in-vivo mouse brain is acquired. Colormap represents fluorescence intensity. (B) From the 2PM data, a graph model is generated in 3 stages described in [31]. Colormap represents nodes’ corresponding vessel size. (C) Particle trajectories are generated using the graph model and in-vivo diameter-velocity dependency. Colormap represents MB velocity. (D) Using a GPU-based US simulator, RF signals are generated and reconstructed to obtain 3D+t US data, on which a correlation-based localization algorithm is applied. Colormap represents the correlation obtained using a spatial convolution of the beamformed PSF and reconstructed in-quadrature (IQ) data.

FIGURE 10. Network filling between density maps at different acquisition times compared to a reference density map of a fully populated vascular network.

research interests include the development of 3D ultrasound techniques for fine imaging of cerebral vascularization.

FIGURE 9. The concentration at which MB count is maximal is depicted as a function of the inverse of the beamformed PSF volume.

FIGURE 4. Example of a simulation conducted with the linear array at 15.625 MHz at different MB concentrations. Localization error was calculated as a function of correlation threshold. Only MB with correlation higher than the threshold were selected. In this specific case, the final threshold for further simulations would be 0.6 to prevent a surge in localization error from interacting MBs.

FIGURE 5. The MB flow simulator is based on two dependencies from [7], namely (Left) MB count vs vessel diameter and (Right) MB velocity vs vessel diameter. Both dependencies are in a logarithmic scale as in [7]. Plots show reference data as a solid black line, raw data as dots, and fitted data as a dashed blue line [7].

FIGURE 6. (Top left) 2D localization error is depicted as a function of microbubble concentration for the 15.625 MHz linear array. (Bottom left) 3D localization error is depicted as a function of microbubble concentration for matrix arrays at various transmit frequencies. (Top right). MB count resulting from localization as a function of concentration is depicted for the 15.625 MHz linear array. (Bottom right) MB count resulting from localization as a function of concentration is depicted for different transmit frequencies using matrix arrays. Bold curves represent the average and shaded areas cover the average + standard deviation of the 6 vascular networks.

TABLE 1. Acquisition parameters. For a specific concentration, localization error was calcu- lated as the average distance between localized MBs and their corresponding closest reference MB. Only the in-plane distances were considered when computing 2D localiza- tion error of the linear array, i.e., the error in the eleva- tion direction was ignored. This process was performed in 2D at 15.625 MHz and in 3D for different transmit fre- quencies spanning current usable range: 3, 3.5, 6, 7, 9 12 and 15 MHz.

FIGURE 2. Particle trajectory generation representation. From a directed graph, a trajectory is selected from an inlet node to an end node. Then, new centerline positions are generated using a velocity-diameter relationship. Finally, from parallel and perpendicular vectors of the centerline trajectory, laminal positions are created.

FIGURE 3. Unique microbubbles positions were randomly distributed in a 10 x 10x10 pattern to span over 5x5 x 6.5 mm. This example shows 1 million MB distributed in 1000 sub-regions, which results in 1000 MB in each sub-region. Even though fewer small vessels are present in each sub-region, this step is essential since the PSF is not uniform in the field of view and it also allows to span the usable MB concentration range. After the ULM framework and metrics computation, MB positions in sub-regions can be added back together in the original size volume to emulate a longer acquisition time for visualization purpos

FIGURE 7. MB positions in 6 vascular networks of a mouse brain. (Top) MB flow was simulated with constraints to follo\ in-vivo dependencies: MB count and velocity with respect to the vessel diameter. (Bottom) MB flow was simulated without the MB count (N) vs vessel diameter (d) constraint. Colormap represents normalized velocity in arbitrary units (A.U.).

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Restoration of Images with Piecewise Space-Variant Blur

by Leah Bar

2007, Lecture Notes in Computer Science

We address the problem of space-variant image deblurring, where different parts of the image are blurred by different blur kernels. Assuming a region-wise space variant point spread function, we first solve the problem for the case of... more

Whenever the contours C; are known a priori, the ¢; functions can easily be
determined. The recovered image f and edge map v are alternately obtained via
the solution of the following Euler-Lagrange equations [2]:
Fig. 3. Non-blind space-variant restoration with different blur kernels in each region.
Left: Blurred image. Right: Restoration using the suggested method.

Fig. 2. Non-blind space-variant restoration. Left column: Spatially variant motion
blurred images. Right column: The corresponding recovered images using the suggested
method.

Fig. 1. Failure of the region-wise image deconvolution algorithm. Left: Spatially variant
blurred image. Right: Restoration using a region-wise algorithm
Consider an image that consists of known sub-domains blurred by known kernels.
It is well known [14] that region-wise deblurring may yield boundary discontinu-
ities. This problem is illustrated in Fig. 1. The 256 x 256 Lena image was blurred
by an 8 pixels horizontal motion blur within the marked rectangular region. This
region was recovered by the Total Variation deconvolution method [19] and put
back into its place in the observed image. The outcome of the region-wise pro-
cedure is shown on the right. It can be easily seen that although the regional
recovery is satisfying, the gray levels on both sides of the boundary are not com-
patible. To solve this problem, some blending constraints have to be added to
the boundary conditions. Moreover, if the region shape is more complex, dealing
with boundaries requires additional algorithmic effort.

Fig. 4. Left: Blurred image. Right: The corresponding E function.

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Imaging skin pathology with polarized light

by Jessica Ramella-Roman

2002, Journal of Biomedical Optics

Linearly polarized light that illuminates skin is backscattered by superficial layers and rapidly depolarized by birefringent collagen fibers. It is possible to distinguish such superficially backscattered light from the total diffusely... more

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Blurred Image Detection and Classification

by Bing-Yu Chen

Lecture Notes in Computer Science

Digital photos are massively produced while digital cameras are becoming popular, however, not every photo has good quality. Blur is one of the conventional image quality degradation which is caused by various factors. In this paper, we... more

Fig. 5. The classification of globally blurred images.

Fig. 2. Left: original images. Middle: gradient magnitude histogram. Right: gradient direction histogram.

Fig. 1. The procedure of the blur detection. Therefore, every image, by our blur detector, can be classified into one of the following five types: non-blurred, camera shake, out of focus, moving object, and depth of field. Fig. 1 shows the procedure of the blur detection.

Fig. 3. Different images and their blur extent values. From 200 blurred images and 200 clear images, half of the images are randomly chosen as the training data, and the remaining images are the predicting data. The gradient magnitude histogram is segmented to a 360 dimensional vector as well as the direction histogram. It turns out that the accuracy is 99.5% since only one image is wrong for 100 blurred images and 100 clear images. Fig. 3 shows some images and their blur extent values.

Fig. 4. Blur region detection. will not be accurate; if the grids are too small, there will be a multitude of fake blurred regions. The width and height of the grid is set to 10% of the image. If the prediction value of the grid is larger than 0.5, it is a blurred region. The non- blurred region, vice versa, are the grids with value less than 0.5. The variance of monochrome identification is heuristically set to 30. It turns out a decision map that can tell where the blurred region is. Every image is segmented to k regions including k, blurred regions, kg non-blurred regions, and k3 fake blurred regions in the decision map. If k,/(k, + k2) > 0.7 , then the image is a globally blurred image, otherwise it is a locally blurred image. Fig. 4 shows the grid structure and the visualization of the prediction result. The image is considered as a locally blurred image because there exist both blurred regions and non-blurred regions.

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Blind restoration of atmospherically degraded images by automatic best step-edge detection

by Omri Shacham and

2007, Pattern Recognition Letters

Image restoration algorithms often require previous knowledge about the point spread function (PSF) of the disturbance. Deriving the PSF manually from a degraded ideal step-edge in the image is a well known procedure intended mainly for... more

Fig. 12. (a) A comparison between the extracted MTFs before and after restoration; (b) The restored image using the MTF estimated from the real-degraded image.

Fig. 6. (a) A comparison between the extracted MTFs before and after restoration and the true MTF; (b) The restored image using the MTF estimated from the degraded image.

Fig. 10. Same as Fig. 4, but for the real-degraded image shown in Fig. 8.

Fig. 7. Results of applying an alternative blind-deconvolution technique show high sensitivity to the initial PSF guess [compare all the results to Fig. 6b]. (a) Restoration using the Richardson—Lucy blind restoration method (after 300 iterations) with initial Gaussian PSF of size 25 x 25 pixels and standard deviation of 3; (b) Same as (a) but with a standard deviation of 2.

Fig. 13. Results of applying an alternative blind-deconvolution technique to the real blurred image show high sensitivity to the initial PSF guess [compare all the results to Fig. 12b]. (a) Restoration using the Richard- son—Lucy blind restoration method (after 20 iterations) with initial Gaussian PSF of size 17 x 17 pixels and standard deviation of 2; (b) Same as (a) but with a standard deviation of 1. “ — For comparison, Fig. 13a and b present the results of implementing the RL blind-deconvolution technique (after 20 iterations) with initial Gaussian PSFs of standard devi- ations 2 and 1, respectively (the Gaussian support size was set to 17 x 17 pixels in both cases). It can be noted that the restored image shown in Fig. 13a is significantly better than the restored image shown in Fig. 13b, and actually quite

Fig. 9. Same as Fig. 3, but for the real-degraded image shown in Fig. 8. Fig. 8. A real degraded image captured by a staring thermal camera, in the 3-5 um wavelength range. the contrast and bi-modality of the local-histograms [Eq. (2)] within square regions of size 17 x 17 pixels around each of the 1070 pixels. The pixel that obtained the highest value is marked by a circle in Fig. 11a. This pixel is the center of

Fig. 1. Example for a chain of edge pixels.

Fig. 3. Results of applying the edge length and straightness criterion to the detected edge pixels of the degraded image shown in Fig. 2b. Higher (brighter) values represent higher length and straightness. (a) Small-scale length and straightness weighting code of the edge pixels; (b) Large-scale length and straightness weighting code of the edge pixels.

Fig. 2. (a) The original image (a monument in Beer Sheva city); (b) The degraded image, created by synthetically blurring the original image of (a) with a Gaussian convolution kernel of an 21 x 21 pixel size and a standard deviation of 3.

A weighting code of small-scale length and straightness evaluation of the edge pixels shown in Fig. | Table 1

Fig. 11. Same as Fig. 5, but for the real-degraded image shown in Fig. 8.

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Optical Quality of the Eye with the Artisan Phakic Lens for the Correction of High Myopia

by Juan M Bueno and

2003, Optometry and Vision Science

Purpose. To evaluate the optical quality of the eye before and after the insertion of an Artisan phakic intraocular lens for the treatment of high myopia. Methods. Consecutive patients implanted with the Artisan lens by a single surgeon... more

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Image restoration by Wiener deconvolution in limited-view computed tomography

by Atam Dhawan

1985, Applied Optics

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Annular Pupils, Radial Polarization, and Superresolution

by Colin Sheppard

2004, Applied Optics

An annular pupil, which can be used to produce a Bessel beam, when combined with radially polarized illumination promises improvements in microscope resolution, increased packing density for optical storage, and finer optical lithography.... more

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Point Spread Function

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