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Adaptive multiple subtraction with waveletbased complex unary Wiener filters
"... Running head: CWT unary adaptive multiple filtering 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 su ..."
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Running head: CWT unary adaptive multiple filtering 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. In this work we focus on the subtraction element. We propose an adaptive multiple removal technique in a 1D complex wavelet frame combined with a nonstationary adaptation performed via singlesample (unary) Wiener filters, consistently estimated on overlapping windows in the transformed domain. This approach greatly simplifies the matching filter estimation 1 and, despite its simplicity, compares promisingly with standard adaptive 2D methods, both in terms of results and retained speed and efficiency. 2
Epigraphical projection and proximal tools for solving constrained convex optimization problems
 Part I,” pp. x+24, 2012, Submitted. Preprint: http://arxiv.org/pdf/1210.5844
"... We propose a proximal approach to deal with convex optimization problems involving nonlinear constraints. A large family of such constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but ..."
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We propose a proximal approach to deal with convex optimization problems involving nonlinear constraints. A large family of such constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For this class of constraints, the associated projection operator generally does not have a closed form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. A closed halfspace constraint is also enforced, in order to limit the sum of the introduced epigraphical variables to the upper bound of the original lower level set. In this paper, we focus on a family of constraints involving linear transforms of ℓ1,p balls. Our main theoretical contribution is to provide closed form expressions of the epigraphical projections associated with the Euclidean norm (p = 2) andthe supnorm (p = +∞). The proposed approach is validated in the context of image restoration with missing samples, by making use of TVlike constraints. Experiments show that our method leads to significant improvements in term of convergence speed over existing algorithms for solving similar constrained problems. 1
COHERENT NOISE REMOVAL IN SEISMIC DATA WITH REDUNDANT MULTISCALE DIRECTIONAL FILTERS
"... Directional filters are commonly used tools in modern seismic data processing to address coherent signals, depending on their apparent slowness or slope. This operation enhances the characterization of the great variety of signals present in a seismic dataset that enables a better characterization o ..."
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Directional filters are commonly used tools in modern seismic data processing to address coherent signals, depending on their apparent slowness or slope. This operation enhances the characterization of the great variety of signals present in a seismic dataset that enables a better characterization of the subsurface structure. This paper compares two complementary local adaptive multiscale directional filters: a directional filter bank based on dualtree Mband wavelets and a novel local slant stack transform (LSST) based filter in the timescale domain. Their differences reside in redundancy levels and slope (directional) resolution. A structural similarity index measure has been employed to objectively compare both approaches on a real seismic dataset example. 1.
A MajorizeMinimize Memory Gradient Method for ComplexValued Inverse Problems
, 2013
"... Complexvalued data are encountered in many application areas of signalandimageprocessing. Inthecontextofoptimizationoffunctions of real variables, subspace algorithms have recently attracted much interest, owing to their efficiency for solving largesize problems while simultaneously offering theor ..."
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Complexvalued data are encountered in many application areas of signalandimageprocessing. Inthecontextofoptimizationoffunctions of real variables, subspace algorithms have recently attracted much interest, owing to their efficiency for solving largesize problems while simultaneously offering theoretical convergence guarantees. The goal of this paper is to show how some of these methods can be successfully extended to the complex case. More precisely, we investigate the properties of the proposed complexvalued MajorizeMinimize Memory Gradient (3MG) algorithm. Important practical applications of these results arise in inverse problems. Here, we focus on image reconstruction in Parallel Magnetic Resonance Imaging (PMRI). The linear operator involved in the observation model then includes a subsampling operator over the kspace (spatial Fourier domain) the choice of which is analyzed through our numerical results. In addition, sensitivity matrices associated with the multiple coil channels come into play. Comparisons with existing optimization methods confirm the good performance of the proposed algorithm.
SUMMARY
"... Multiple attenuation is one of the greatest challenges in seismic processing. Due to the high crosscorrelation between primaries and multiples, attenuating the latter without distorting the former is a complicated problem. We propose here a joint multiple modelbased adaptive subtraction, using sin ..."
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Multiple attenuation is one of the greatest challenges in seismic processing. Due to the high crosscorrelation between primaries and multiples, attenuating the latter without distorting the former is a complicated problem. We propose here a joint multiple modelbased adaptive subtraction, using singlesample 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 realfield data, with a singlemodel adaptation and a combination of several multiple models.
Abstract Physically Unclonable Functions (PUFs) are
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Contents lists available at ScienceDirect Simulation Modelling Practice and Theory
"... journal homepage: www.elsevier.com/locate/simpat Performance analysis of a thresholdbased discretetime queue ..."
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journal homepage: www.elsevier.com/locate/simpat Performance analysis of a thresholdbased discretetime queue
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 timevarying filtering, compensating ina ..."
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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 timevarying filtering, compensating inaccuracies in given approximate templates. The underdetermined 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.
i m e
"... Unary adaptive subtraction of joint multiple models with complex wavelet frames TaM0: Nonstationary, waveletbased, adaptive multiple removal TaM1: “Complex ” wavelet transform + simple onetap (unary) filter TaM2: Redundancy selection: noise robustness and processing speed TaM3: Smooth adaptation ..."
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Unary adaptive subtraction of joint multiple models with complex wavelet frames TaM0: Nonstationary, waveletbased, adaptive multiple removal TaM1: “Complex ” wavelet transform + simple onetap (unary) filter TaM2: Redundancy selection: noise robustness and processing speed TaM3: Smooth adaptation to adaptive joint multiple model filtering