Multiple Filtering

We develop a method to match estimates of primaries and multiples to data containing both. It works with prestack data in either data space or image space and addresses the well-known issue of cross-talk between the estimates of the primaries and the multiples. The method iteratively computes non-stationary filters with micro-patches and its cost is a negligible fraction of the cost of computing the estimates of the primaries and multiples with SRME. We show, with several synthetic and real data examples, that the matched estimates of both primaries and multiples are essentially free of cross-talk. We also apply the method to the separation of ground-roll and body waves and show that most residual ground-roll contaminating the estimate of the body waves can be eliminated.

This paper compares two different approaches to attenuate surface related multiples, i.e., the minimum energy wavelet extraction and the adaptive subtraction with 1D matching filter. Results on Sigsbee2B synthetic data are illustrated to demonstrate the effectiveness of both methods.

Adaptive subtraction is a key element in predictive multiple-suppression methods. It minimizes misalignments and amplitude differences between modeled and actual multiples, and thus reduces multiple contamination in the data set after subtraction. Due to the high crosscorrelation between their waveforms, the main challenge resides in attenuating multiples without distorting primaries. As they overlap on a wide frequency range, we split this wide-band problem into a set of more tractable narrow-band filter designs, using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via complex, single-sample (unary) Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates for amplitude differences within its frequency support, and can correct small and large misalignment errors through phase and integer delay corrections. This approach greatly simplifies the matching filter estimat...

Multiple attenuation is a crucial task in seismic data processing because multiples usually cover primaries from fundamental reflectors. Predictive multiple suppression methods remove these multiples by building an adapted model, aiming at being subtracted from the original signal. However, before the subtraction is applied, a matching filter is required to minimize amplitude differences and misalignments between multiples and their prediction, and thus to minimize the multiples in the input dataset after the subtraction. In this paper we focus on the subtraction element. The proposed complex wavelet transform based approach simplifies the matching filter estimation.

The local slant-stack transform (LSST) is a technique commonly used in seismic data processing to filter complex seismic waves, when the τ-p transform and the f-k filters cannot be used. To automatically adapt the characteristics of the filters based on the LSST to the slowness variation of the wavefronts in seismic profiles these filters are usually combined with an instantaneous slowness estimator. To make an objective design, we analyze the relation between the slowness resolution, the window parameters and the main frequency components of the waves to employ the most suitable windows in order to achieve an optimum slowness and space resolutions. We further validate this design procedure with two synthetic examples.

We propose a curvelet domain strategy to subtract ground-roll from seismic records. We built curvelet domain mask functions from higher scales which are groud-roll-free and project them to the lower scales that are contaminated with ground-roll energy. The mask function helps to preserve the reflected energy and eliminate the ground-roll energy. A synthetic seismic data example is provided to analyze the performance of the proposed method.

Due to complex subsurface structure properties, seismic records often suffer from coherent noises such as multiples. These undesired signals may hide the signal of interest, thus raising difficulties in interpretation. We propose a new variational framework based on Maximum A Posteriori (MAP) estimation. More precisely, the problem of multiple removal is formulated as a minimization problem involving time-varying filters, assuming that a disturbance signal template is available and the target signal is sparse in some orthonormal basis. We show that estimating multiples is equivalent to identifying filters and we propose to employ recently proposed convex optimization procedures based on proximity operators to solve the problem. The performance of the proposed approach as well as its robustness to noise is demonstrated on realistically simulated data.

The central insight that comes from the work of Berkhout, Verschuur and others in the development of their method for surface-related multiple elimination (SRME) is that multiples, normally considered as unwanted noise in seismic data, are intimately related to, and can be constructed from, primary reflections. It follows that multiples contain equivalent information about the subsurface to that which is given by the primaries. There are circumstances, therefore, in which the multiples can add to signal, i.e. they can be an aid to seismic processing and interpretation rather than being viewed simply as unwelcome noise. In this paper I first present an approach to multiple removal in shallow water that is a wavefield-consistent form of multi-channel prediction-error filtering. This is an alternative to inversion-based or iterative approaches to SRME in shallow-water applications where these methods encounter difficulties due to missing near-offsets. The multi-channel prediction filters are themselves estimates of the near-offset water-bottom reflection, derived from the primaries and multiples that are present at the available offsets. I use these prediction operators (equivalently, the estimated water-bottom reflection) to derive an inverse operator that, in the spirit of the focal transform operator described by Berkhout and Verschuur, can construct primary reflections from multiples. As with SRME, the focal transform also encounters difficulties in shallow water due to missing near offsets. The prediction operators provide a way of overcoming this limitation and supply the additional information needed to successfully reconstruct primaries from multiples in shallow water.

The central insight that comes from the work of Berkhout, Verschuur and others in the development of their method for surface-related multiple elimination (SRME) is that multiples, normally considered as unwanted noise in seismic data, are intimately related to, and can be constructed from, primary reflections. It follows that multiples contain equivalent information about the subsurface to that which is given by the primaries. There are circumstances, therefore, in which the multiples can add to signal, i.e. they can be an aid to seismic processing and interpretation rather than being viewed simply as unwelcome noise. In this paper I first present an approach to multiple removal in shallow water that is a wavefield-consistent form of multi-channel prediction-error filtering. This is an alternative to inversion-based or iterative approaches to SRME in shallow-water applications where these methods encounter difficulties due to missing near-offsets. The multi-channel prediction filters are themselves estimates of the near-offset water-bottom reflection, derived from the primaries and multiples that are present at the available offsets. I use these prediction operators (equivalently, the estimated water-bottom reflection) to derive an inverse operator that, in the spirit of the focal transform operator described by Berkhout and Verschuur, can construct primary reflections from multiples. As with SRME, the focal transform also encounters difficulties in shallow water due to missing near offsets. The prediction operators provide a way of overcoming this limitation and supply the additional information needed to successfully reconstruct primaries from multiples in shallow water.

The surface-related multiple elimination (SRME) method has proven to be successful on a large number of data cases. Most of the applications are still 2D, as the full 3D implementation is still expensive and under development. However, the earth is a 3D medium, such that 3D effects are difficult to avoid. Most of the 3D effects come from diffractive structures, whereas the specular reflections normally have less of a 3D behavior. By separating the seismic data in a specular reflecting and a diffractive part, multiple prediction can be carried out with these different subsets of the input data, resulting in several categories of predicted multiples. Because each category of predicted multiples can be subtracted from the input data with different adaptation filters, a more flexible SRME procedure is obtained. Based on some initial results from a Gulf of Mexico dataset, the potential of this approach is investigated. Figure 4: Example of curvelet-based removal of multiples using either all predicted multiples in one thresholding process (b) versus the result of using each of the four categories of predicted multipels in a separate thresholding procedure. Note the improved suppression of the diffracted multiples in the latter case (e.g. at the arrows). Also observe the cleaner appearance of the time slice in (c).

In this abstract, we present a nonlinear curvelet-based sparsitypromoting formulation for the primary-multiple separation problem. We show that these coherent signal components can be separated robustly by explicitly exploting the locality of curvelets in phase space (space-spatial frequency plane) and their ability to compress data volumes that contain wavefronts. This work is an extension of earlier results and the presented algorithms are shown to be stable under noise and moderately erroneous multiple predictions.

Seismic acquisition is confined by limited aperture that leads to finite illumination, which, together with other factors, hinders imaging of subsurface objects in complex geological settings such as salt structures. Conventional processing, including surface-related multiple elimination, further reduces the amount of information we can get from seismic data. With the growing consensus that multiples carry valuable information that is missing from primaries, we are motivated to exploit the extra illumination provided by multiples to image the subsurface. In earlier research, we proposed such a method by combining primary estimation and sparsity-promoting migration to invert for model perturbations directly from the total up-going wavefield. In this abstract, we focus on a particular case. By exploiting the extra illumination from surface-related multiples, we mitigate the effects caused by migrating from incomplete data with missing sources and missing near-offsets.

In many exploration areas, successful separation of primaries and multiples greatly determines the quality of seismic imaging. Despite major advances made by surface-related multiple elimination (SRME), amplitude errors in the predicted multiples remain a problem. When these errors vary for each type of multiple in different ways (as a function of offset, time, and dip), they pose a serious challenge for conventional least-squares matching and for the recently introduced separation by curvelet-domain thresholding. We propose a data-adaptive method that corrects amplitude errors, which vary smoothly as a function of location, scale (frequency band), and angle. With this method, the amplitudes can be corrected by an elementwise curvelet-domain scaling of the predicted multiples. We show that this scaling leads to successful estimation of primaries, despite amplitude, sign, timing, and phase errors in the predicted multiples. Our results on synthetic and real data show distinct improve...

I consider the problem of finding the impulse response, or Green's function, from a measured response including noise, given an estimate of the source time function. This process is usually known as signature deconvolution. Classical signature deconvolution provides no measure of the quality of the result and does not separate signal from noise. Recovery of the earth impulse response is here formulated as the calculation of a Wiener filter in which the estimated source signature is the input and the measured response is the desired output. Convolution of this filter with the estimated source signature is the part of the measured response that is correlated with the estimated signature. Subtraction of the correlated part from the measured response yields the estimated noise, or the uncorrelated part. The fraction of energy not contained in this uncorrelated component is defined as the quality of the filter. If the estimated source signature contains errors, the estimated earth impulse response is incomplete, and the estimated noise contains signal, recognizable as trace-to-trace correlation. The method can be applied to many types of geophysical data, including earthquake seismic data, exploration seismic data, and controlled source electromagnetic data; it is illustrated here with examples of marine seismic and marine transient electromagnetic data.

A non-linear primary-multiple separation method using curvelets frames is presented. The advantage of this method is that curvelets arguably provide an optimal sparse representation for both primaries and multiples. As such curvelets frames are ideal candidates to separate primaries from multiples given inaccurate predictions for these two data components. The method derives its robustness regarding the presence of noise; errors in the prediction and missing data from the curvelet frame's ability (i) to represent both signal components with a limited number of multi-scale and directional basis functions; (ii) to separate the components on the basis of differences in location, orientation and scales and (iii) to minimize correlations between the coefficients of the two components. A brief sketch of the theory is provided as well as a number of examples on synthetic and real data. for p = 1 or p = 2. Given an estimate for a(t), the primaries d0(xr,xs,t) are calculated according E...

In many exploration areas, successful separation of primaries and multiples greatly determines the quality of seismic imaging. Despite major advances made by surface-related multiple elimination (SRME), amplitude errors in the predicted multiples remain a problem. When these errors vary for each type of multiple in different ways (as a function of offset, time, and dip), they pose a serious challenge for conventional least-squares matching and for the recently introduced separation by curvelet-domain thresholding. We propose a data-adaptive method that corrects amplitude errors, which vary smoothly as a function of location, scale (frequency band), and angle. With this method, the amplitudes can be corrected by an elementwise curvelet-domain scaling of the predicted multiples. We show that this scaling leads to successful estimation of primaries, despite amplitude, sign, timing, and phase errors in the predicted multiples. Our results on synthetic and real data show distinct improve...

Copyright 2012, SBGf-Sociedade Brasileira de Geofísica Este texto foi preparado para a apresentação no V Simpósio Brasileiro de Geofísica, Salvador, 27 a 29 de novembro de 2012. Seu conteúdo foi revisado pelo Comitê Técnico do V SimBGf, mas não necessariamente representa a opinião da SBGf ou de seus associados. É proibida a reprodução total ou parcial deste material para propósitos comerciais sem prévia autorização da SBGf.

Contents of this paper were reviewed by the Technical Committee of the 13 th International Congress of The Brazilian Geophysical Society and do not necessarily represent any position of the SBGf, its officers or members. Electronic reproduction or storage of any part of this paper for commercial purposes without the written consent of The Brazilian Geophysical Society is prohibited.

The removal and use of multiples have a single shared goal and objective: the imaging and inversion of primaries. There are two kinds of primaries: recorded primaries and unrecorded primaries. For imaging recorded primaries using an industry standard practice smooth velocity model, recorded multiples must be removed, to avoid false and misleading images due to the multiples. Similarly, to find an approximate image of an unrecorded primary, that is a subevent of a recorded multiple, unrecorded multiples that are subevents of the recorded multiple must be removed, for exactly the same problem and reason that recorded multiples are needed to be eliminated. Direct inverse methods are employed to derive this new comprehensive perspective on primaries and multiples. Direct inverse methods not only assure that the problem of interest is solved, but equally important, that the problem of interest is the relevant problem that we (the petroleum industry) need to be interested in.

Blended acquisition has become popular due to its high efficiency and low cost. In conventional processing procedure, overlapping seismic data need to be separated as if they were acquired through the unblended way before primary estimation which is time-consuming. Given this situation, we utilize the recently introduced algorithm closed-loop SRME based on 3D L1-norm sparse inversion methodology, in which primaries of the deblended shot records can be directly estimated from the blended data. With the introduction of the blended operator to this technique, a link is made between the blended and conventional acquisition. A one-step inversion is proposed, achieving simultaneous seismic deblending and primary estimation. Preliminary results of synthetic data are promising.

Multiple attenuation is one of the greatest challenges in seismic processing. Due to the high cross-correlation between primaries and multiples, attenuating the latter without distorting the former is a complicated problem. We propose here a joint multiple model-based adaptive subtraction, using single-sample unary filters' estimation in a complex wavelet transformed domain. The method offers more robustness to incoherent noise through redundant decomposition. It is first tested on synthetic data, then applied on real-field data, with a single-model adaptation and a combination of several multiple models.

Adaptive subtraction is a key element in predictive multiple-suppression methods. It minimizes misalignments and amplitude differences between modeled and actual multiples, and thus reduces multiple contamination in the dataset after subtraction. Due to the high crosscorrelation between their waveform, the main challenge resides in attenuating multiples without distorting primaries. As they overlap on a wide frequency range, we split this wide-band problem into a set of more tractable narrow-band filter designs, using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via complex, single-sample (unary) Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates amplitude differences within its frequency support, and can correct small and large misalignment errors through phase and integer delay corrections. This approach greatly simplifies the matching filter estimation and, despite its simplicity, narrows the gap between 1D and standard adaptive 2D methods on field data * .

This paper introduces a fully data-driven concept, multiple prediction through inversion (MPI), for surface-related multiple attenuation (SMA). It builds the multiple model not by spatial convolution, as in a conventional SMA, but by updating the attenuated multiple wavefield in the previous iteration to generate a multiple prediction for the new iteration, as is usually the case in an iterative inverse problem. Because MPI does not use spatial convolution, it is able to minimize the edge effect that appears in conventional SMA multiple prediction and to eliminate the need to synthesize near-offset traces, required by a conventional scheme, so that it can deal with a seismic data set with missing near-offset traces. The MPI concept also eliminates the need for an explicit surface operator, which is required by conventional SMA and is comprised of the inverse source signature and other effects. This method accounts implicitly for the spatial variation of the surface operator in multiple-model building and attempts to predict multiples which are not only accurate kinematically but are also accurate in phase and amplitude.

In this article, we propose an inversion scheme to replace the adaptive subtraction approaches which are widely used in conventional two-step (prediction + subtraction) multiple elimination methods. This new method, named SIMP (simultaneous inversion for multiples and primaries), inverts seismic data using constraints (e.g., modeled multiples and/or geologic discriminants) for multiples and primaries simultaneously. SIMP incorporates pattern recognition and shaping filters into one concise and practically solvable formulation. Its main advantages are that no orthogonality between multiples and primaries is assumed and that wavelet information is not necessary for the inversion. Figure 1 compares conventional prediction plus subtraction and the SIMP approaches. In the conventional method (Figure 1a), predicted multiples are generated first, the shaping filters are derived second, and finally the primary component is obtained by subtracting the multiples shaped by the filters from the input data. In one SIMP procedure (SIMP I, Figure 1b), the predicted multiples are generated first, but the shaping filters (not the multiples) and the primaries are inverted simultaneously by a constrained inversion approach. A general SIMP approach (SIMP II, Figure 1c) inverts for multiples and primaries simultaneously assuming proper constraints are available. Modern multiple elimination methodologies are firmly rooted in the principles of wave theory. In general, these multiple removal schemes involve two basic steps: multiple prediction and adaptive subtraction. The multiple prediction can be model-driven or data-driven. During the prediction step, the kinematic part of the multiples (traveltimes) is obtained. The adaptive subtraction step aims to obtain the dynamic part of the multiples (e.g., amplitudes and wave-form shaping). Once multiple-model traces are predicted, based on the original seismic data and/or a subsurface model, they need to be " shaped " in order to " match " the actual multiples. This is usually achieved with an adaptive least-squares subtraction approach and the matching filter may be represented as where y(t) is a raw data trace, m(t) are modeled multiple traces, N is the number of channels involved in matching, f(t) are operators for adapting the group of N traces m(t) to the desired output y(t), * indicates convolution, and p(t) is the matching residual (primaries). The filter coefficients, f(t), are calculated using the well-known minimum-energy criterion. The fundamental problem with minimizing the energy of the primary p(t) is the assumption that multiples and primaries in the data are orthogonal. This assumption will be violated in most field data sets and, consequently, primaries overlapping modeled multiples will be wrongly subtracted from the data. Thus, a " leakage " will always be present. To overcome this problem , Spitz (1999) proposed a " pattern recognition " subtraction based on prediction error filters (PEF). In the following, we start from shaping filtering concepts and develop a concise formulation that does not require the orthogonal assumption. After that, a more general formula is developed to estimate multiples and primaries by using PEF, instead of explicitly modeled multiples. This is similar to Spitz's pattern recognition work but has the flexibility to incorporate more constraints in a systematic fashion. Theoretical development. The system of equations in (1) is highly underdetermined since both f(t) and p(t) are unknown. To avoid this problem, multichannel Wiener filtering is traditionally used to minimize the following misfit function: After some routine treatment in the least-squares sense, the minimization problem above yields the following linear system of equations: M is a matrix with N columns of vectors which are win-dowed seismic traces, Y is a vector whose elements are

This paper compares two different approaches to attenuate surface related multiples, i.e., the minimum energy wavelet extraction and the adaptive subtraction with 1D matching filter. Results on Sigsbee2B synthetic data are illustrated to demonstrate the effectiveness of both methods.

In this paper we present a method of multiple attenuation in the plane wave domain that uses a filter estimation procedure to match the angle dependent primaries to predict the observed multiples. The filter is obtained through the solution of an optimization problem. Instead of using a source function estimate we use the primaries from the shallow part of the data (reflectivity) to estimate the multiples associated with these events that are correct in traveltime, but not necessarily in amplitude. Using this filter the amplitude and phase of the multiples are estimated and the predicted multiples are subtracted from the data to obtain multiple free data. The application of this method is illustrated on synthetic and real data and the results demonstrate its effectiveness in attenuating multiples. The proposed method is computationally very efficient.

The ℓ 1 /ℓ 2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the ℓ 1 /ℓ 2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the ℓ 1 /ℓ 2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact ℓ 1 /ℓ 2 term, on an application to seismic data blind deconvolution. * Université Paris-Est, LIGM, CNRS-UMR 8049. † IFP Energies nouvelles.

Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation is obtained through time-varying filtering, compensating inaccuracies in given approximate templates. The under-determined problem can then be formulated as a convex optimization one, providing estimates of both filters and primaries. Within this framework, the criterion to be minimized mainly consists of two parts: a data fidelity term and hard constraints modeling a priori information. This formulation may avoid, or at least facilitate, some parameter determination tasks, usually difficult to perform in inverse problems. Not only classical constraints, such as sparsity, are considered here, but also constraints expressed through hyperplanes, onto which the projection is easy to compute. The latter constraints lead to improved performance by further constraining the space of geophysically sound solutions.

SUMMARY Multiple attenuation is a crucial task in seismic data processing because multiples usually cover primaries from fundamental reflectors. Predictive multiple suppression methods remove these multiples by building an adapted model, aiming at being subtracted from the original signal. However, before the subtraction is applied, a matching filter is required to minimize amplitude differences and misalignments between multiples and their prediction, and thus to minimize the multiples in the input dataset after ...

In oil painting restoration, masterpieces dirtied by centuries of grime and smoke are cleaned to reveal the original brilliant image. The recent cleaning and restoration of the frescoes in the Sistine Chapel are a familiar example. Once the unwanted dirt had been removed, the beauty and vibrant colors of the true image was stunning. The splendor of the true image had been there all the time, unseen and obscured by 'noise', for years. The restoration renewed the vivid colors of Michelangelo's work, and, in fact, caused art historians to reconsider their understanding of the master's use of color.

The simultaneous firing of marine sources can provide a significant uplift in terms of acquisition efficiency and data quality enhancement. However, the seismic interference resulting from one or more 'other' sources needs to be well understood and the appropriate processing strategies need to be developed for the method to fulfil its promise.

Le filtrage adaptatif est une pièce importante des méthodes de suppression de multiples.  Elle permet de réduire les décalages et des différences d'amplitude entre des modèles de multiples et les multiples réels, permettant de réduire leur contamination des données sismiques. Etant très corrélés avec les formes d'ondes présentes dans les primaires, l'enjeu est d'atténuer les multiples sans distordre les données primaires. Afin de simplifier le calcul de filtres adaptés sur une bande de fréquence large, une trame d'ondelettes complexes découpe le signal en voies à bande de fréquence étroite. Cette représentation permet d'effectuer la soustraction adaptative en une passe, avec de simples filtres de Wiener unaires, c'est-à-dire réduits à un unique coefficient complexe. Afin de tenir compte des non-stationnarités, le calcul s'effectue dans le plan temps-échelle complexe, le long de fenêtres glissantes.

Chaque filtre unaire compense des écarts d'amplitude et des décalages faibles et plus importants, via des corrections de phase et de délai entier, dans une bande de fréquence très étroite. Cette approche simplifie grandement l'estimation du filtre adapté, et fournit, même en 1D, des résultats comparables à des approches 2D classiques, à un coût de calcul très compétitif.

Adaptive multiple subtraction with wavelet-based complex unary Wiener filters, S. Ventosa, S. Le Roy, Irène Huard, A. Pica, H. Rabeson, P. Ricarte, L. Duval, Geophysics, number 77, vol. 183, p. 183-192, Nov.-Dec. 2012
http://arxiv.org/abs/1108.4674

Abstract: Multiple attenuation is a crucial task in seismic data processing because multiples usually cover primaries from fundamental reflectors. Predictive multiple suppression methods remove these multiples by building an adapted model, aiming at being subtracted from the original signal. However, before the subtraction is applied, a matching filter is required to minimize amplitude differences and misalignments between actual multiples and their prediction, and thus to minimize multiples in the input dataset after the subtraction.

ABSTRACT Due to complex subsurface structure properties, seismic records often suffer from coherent noises such as multiples. These undesired signals may hide the signal of interest, thus raising difficulties in interpretation. We propose a new variational framework based on Maximum A Posteriori (MAP) estimation.

Reducing multiple contamination \citep{Verschuur_D_1992_j-geophysics_ada_srme,Matson_K_2005_j-tle_int_ssma}
represents one of the greatest challenges in seismic processing. Two major aspects differentiate multiples and primary reflections: (1)
the velocity of primaries is greater than that of multiples, and (2)
multiples are periodic events in contrast with primaries. We can hence
classify multiple attenuation methods into two broad categories: \emph{filtering
methods} that find a differentiating feature in the primary and the
multiple \citep{Kelamis_P_2008_p-eage_two_paalm}; and \emph{predictive
suppression methods} that first predict and then subtract the multiple
events from original seismic data \citep{Pica_A_2005_j-tle_3d_srmm,Weisser_T_2006_j-fb_wav_emmai3dsrme}.
Alas, no single approach fits all scenarios. Most contractors thus
propose an extensive portfolio of demultiple algorithms that, in practice,
may be combined and cascaded to obtain acceptable solutions.

Predictive multiple suppression methods consist of two main elements:
prediction and subtraction. Prediction builds a multiple estimation
from the primaries using prior knowledge. Subtraction minimizes
amplitude difference and  small misalignment between actual multiple
events and their predicted models, to maximize multiple attenuation
in the input dataset. The efficiency of this suppression  strongly
depends on the adaptation capability of the matching filter employed
in the subtraction element. In the following we will focus on the
enhancement of the latter  key element.


Primaries and  multiples are not fully uncorrelated,
as they are generated from the same source. This poses a major challenge in the design of an optimal matching filter to
minimize the multiple events in the input dataset from their predicted
model. Slight differences in their spectra may be exploited with 
wavelet-based approaches \citep{Pokrovskaia_T_2004_p-eage_att_rmcnwtd,Ahmed_I_2007_p-eage_ada_ms2dwtd,Neelamani_R_2008_p-eage_ada_scct}.
The present paper follows a similar  trail, with a twist towards filter
adaptation.

Reducing multiple contamination \citep{Verschuur_D_1992_j-geophysics_ada_srme,Matson_K_2005_j-tle_int_ssma}
represents one of the greatest challenges in seismic processing. Two major aspects differentiate multiples and primary reflections: (1)
the velocity of primaries is greater than that of multiples, and (2)
multiples are periodic events in contrast with primaries. We can hence
classify multiple attenuation methods into two broad categories: \emph{filtering
methods} that find a differentiating feature in the primary and the
multiple \citep{Kelamis_P_2008_p-eage_two_paalm}; and \emph{predictive
suppression methods} that first predict and then subtract the multiple
events from original seismic data \citep{Pica_A_2005_j-tle_3d_srmm,Weisser_T_2006_j-fb_wav_emmai3dsrme}.
Alas, no single approach fits all scenarios. Most contractors thus
propose an extensive portfolio of demultiple algorithms that, in practice,
may be combined and cascaded to obtain acceptable solutions.

Predictive multiple suppression methods consist of two main elements:
prediction and subtraction. Prediction builds a multiple estimation
from the primaries using prior knowledge. Subtraction minimizes
amplitude difference and  small misalignment between actual multiple
events and their predicted models, to maximize multiple attenuation
in the input dataset. The efficiency of this suppression  strongly
depends on the adaptation capability of the matching filter employed
in the subtraction element. In the following we will focus on the
enhancement of the latter  key element.


Primaries and  multiples are not fully uncorrelated,
as they are generated from the same source. This poses a major challenge in the design of an optimal matching filter to
minimize the multiple events in the input dataset from their predicted
model. Slight differences in their spectra may be exploited with 
wavelet-based approaches \citep{Pokrovskaia_T_2004_p-eage_att_rmcnwtd,Ahmed_I_2007_p-eage_ada_ms2dwtd,Neelamani_R_2008_p-eage_ada_scct}.
The present paper follows a similar  trail, with a twist towards filter
adaptation.

Multiple attenuation is one of the greatest challenges in seismic processing. Due to the high cross-correlation between primaries and multiples, attenuating the latter without distorting the former is a complicated problem. We propose here a joint multiple model-based adaptive subtraction, using single-sample unary filters  estimation in a complex wavelet transformed domain. The method offers more robustness to incoherent noise through redundant decomposition. It is first tested on synthetic data, then applied on real-field data, with a single-model adaptation and a combination of several multiple models.

Multiple attenuation is one of the greatest challenges in seismic processing.
Due to the high cross-correlation between primaries and multiples, attenuating the latter without distorting the former is a complicated problem.
We propose here a joint multiple model-based adaptive subtraction, using single-sample unary filters' estimation in a complex wavelet transformed domain.
The method offers more robustness to incoherent noise through redundant decomposition. It is first tested on synthetic data, then applied on real-field data, with a single-model adaptation and a combination of several multiple models.

Limited depth of eld is an important problem in microscopy imaging. 3D objects are often thicker than the depth of eld of the microscope, which means that it is optically impossible to make one single sharp image of them. Instead, different images in which each time a different area of the object is in focus have to be fused together. In this work, we propose a curvelet-based image fusion method that is frequency-adaptive. Because of the high directional sensitivity of the curvelet transform (and consequentially, its extreme sparseness), the average performance gain of the new method over state-of-the-art methods is high.

Reducing multiple contamination (Verschuur and Berkhout, 1992; Matson and Dragoset, 2005) represents
one of the greatest challenges in seismic processing. Two major aspects differentiate multiples
and primary reflections: (1) the velocity of primaries is greater than that of multiples, and (2) multiples
are periodic events in contrast with primaries. We can hence classify multiple attenuation methods into
two broad categories: filtering methods that find a differentiating feature in the primary and the multiple
(Kelamis et al., 2008); and predictive suppression methods that first predict and then subtract the multiple
events from original seismic data (Pica et al., 2005; Weisser et al., 2006). Alas, no single approach
fits all scenarios. Most contractors thus propose an extensive portfolio of demultiple algorithms that, in
practice, may be combined and cascaded to obtain acceptable solutions.
Predictive multiple suppression methods consist of two main elements: prediction and subtraction. Prediction
builds a multiple estimation from the primaries using prior knowledge. Subtraction minimizes
amplitude difference and small misalignment between actual multiple events and their predicted models,
to maximize multiple attenuation in the input dataset. The efficiency of this suppression strongly
depends on the adaptation capability of the matching filter employed in the subtraction element. In the
following we will focus on the enhancement of the latter key element.
Primaries and multiples are not fully uncorrelated, as they are generated from the same source. This
poses a major challenge in the design of an optimal matching filter to minimize the multiple events
in the input dataset from their predicted model. Slight differences in their spectra may be exploited
with wavelet-based approaches (Pokrovskaia and Wombell, 2004; Ahmed et al., 2007; Neelamani et al.,
2008). The present paper follows a similar trail, with a twist towards filter adaptation.