A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

A proximal iteration for deconvolving Poisson noisy images using sparse representations

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a {\it non-linear} degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. $\ell_1$-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy

Basis Pursuit Receiver Function

Receiver functions (RFs) are derived by deconvolution of the horizontal (radial or transverse) component of ground motion from the vertical component, which segregates the PS phases. Many methods have been proposed to employ deconvolution in frequency as well as in time domain. These methods vary in their approaches to impose regularization that addresses the stability problem. Here, we present application of a new time-domain deconvolution technique called basis pursuit deconvolution (BPD) that has recently been applied to seismic exploration data. Unlike conventional deconvolution methods, the BPD uses an L1 norm constraint on model reflectivity to impose sparsity. In addition, it uses an overcomplete wedge dictionary based on a dipole reflectivity series to define model constraints, which can achieve higher resolution than that obtained by the traditional methods. We demonstrate successful application of BPD based RF estimation from synthetic data for a crustal model with a near-surface thin layer of thickness 5, 7, 10, and 15 km. The BPD can resolve these thin layers better with much improved signal-to-noise ratio than the conventional methods. Finally, we demonstrate application of the BPD receiver function (BPRF) method to a field dataset from Kutch, India, where near-surface sedimentary layers are known to be present. The BPRFs are able to resolve reflections from these layers very well.Jackson Chair funds at the Jackson School of Geosciences, University of Texas, AustinCouncil of Scientific and Industrial Research twelfth five year plan project at the Council of Scientific and Industrial Research National Geophysical Research Institute (CSIR-NGRI), HyderabadInstitute for Geophysic

A Fast Blind Impulse Detector for Bernoulli-Gaussian Noise in Underspread Channel

The Bernoulli-Gaussian (BG) model is practical to characterize impulsive noises that widely exist in various communication systems. To estimate the BG model parameters from noise measurements, a precise impulse detection is essential. In this paper, we propose a novel blind impulse detector, which is proven to be fast and accurate for BG noise in underspread communication channels.Comment: v2 to appear in IEEE ICC 2018, Kansas City, MO, USA, May 2018 Minor erratums added in v

Bayesian orthogonal component analysis for sparse representation

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A non-informative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on under-complete dictionary is finally investigated.Comment: Revised version. Accepted to IEEE Trans. Signal Processin