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

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

Abstract—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. Index Terms—Convex optimization, Parallel algorithms, Wavelet transforms, Adaptive filters, Geophysical signal processing, Signal restoration, Sparsity, Signal separation

Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

Robust density modelling using the student's t-distribution for human action recognition

The extraction of human features from videos is often inaccurate and prone to outliers. Such outliers can severely affect density modelling when the Gaussian distribution is used as the model since it is highly sensitive to outliers. The Gaussian distribution is also often used as base component of graphical models for recognising human actions in the videos (hidden Markov model and others) and the presence of outliers can significantly affect the recognition accuracy. In contrast, the Student's t-distribution is more robust to outliers and can be exploited to improve the recognition rate in the presence of abnormal data. In this paper, we present an HMM which uses mixtures of t-distributions as observation probabilities and show how experiments over two well-known datasets (Weizmann, MuHAVi) reported a remarkable improvement in classification accuracy. © 2011 IEEE

Proceedings of the International Workshop on Medical Ultrasound Tomography: 1.- 3. Nov. 2017, Speyer, Germany

Ultrasound Tomography is an emerging technology for medical imaging that is quickly approaching its clinical utility. Research groups around the globe are engaged in research spanning from theory to practical applications. The International Workshop on Medical Ultrasound Tomography (1.-3. November 2017, Speyer, Germany) brought together scientists to exchange their knowledge and discuss new ideas and results in order to boost the research in Ultrasound Tomography

Advancements and Breakthroughs in Ultrasound Imaging

Ultrasonic imaging is a powerful diagnostic tool available to medical practitioners, engineers and researchers today. Due to the relative safety, and the non-invasive nature, ultrasonic imaging has become one of the most rapidly advancing technologies. These rapid advances are directly related to the parallel advancements in electronics, computing, and transducer technology together with sophisticated signal processing techniques. This book focuses on state of the art developments in ultrasonic imaging applications and underlying technologies presented by leading practitioners and researchers from many parts of the world

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Sparse representation frameworks for inference problems in visual sensor networks

Visual sensor networks (VSNs) form a new research area that merges computer vision and sensor networks. VSNs consist of small visual sensor nodes called camera nodes, which integrate an image sensor, an embedded processor, and a wireless transceiver. Having multiple cameras in a wireless network poses unique and challenging problems that do not exist either in computer vision or in sensor networks. Due to the resource constraints of the camera nodes, such as battery power and bandwidth, it is crucial to perform data processing and collaboration efficiently. This thesis presents a number of sparse-representation based methods to be used in the context of surveillance tasks in VSNs. Performing surveillance tasks, such as tracking, recognition, etc., in a communication-constrained VSN environment is extremely challenging. Compressed sensing is a technique for acquiring and reconstructing a signal from small amount of measurements utilizing the prior knowledge that the signal has a sparse representation in a proper space. The ability of sparse representation tools to reconstruct signals from small amount of observations fits well with the limitations in VSNs for processing, communication, and collaboration. Hence, this thesis presents novel sparsity-driven methods that can be used in action recognition and human tracking applications in VSNs. A sparsity-driven action recognition method is proposed by casting the classification problem as an optimization problem. We solve the optimization problem by enforcing sparsity through ł1 regularization and perform action recognition. We have demonstrated the superiority of our method when observations are low-resolution, occluded, and noisy. To the best of our knowledge, this is the first action recognition method that uses sparse representation. In addition, we have proposed an adaptation of this method for VSN resource constraints. We have also performed an analysis of the role of sparsity in classi cation for two different action recognition problems. We have proposed a feature compression framework for human tracking applications in visual sensor networks. In this framework, we perform decentralized tracking: each camera extracts useful features from the images it has observed and sends them to a fusion node which collects the multi-view image features and performs tracking. In tracking, extracting features usually results a likelihood function. To reduce communication in the network, we compress the likelihoods by first splitting them into blocks, and then transforming each block to a proper domain and taking only the most significant coefficients in this representation. To the best of our knowledge, compression of features computed in the context of tracking in a VSN has not been proposed in previous works. We have applied our method for indoor and outdoor tracking scenarios. Experimental results show that our approach can save up to 99.6% of the bandwidth compared to centralized approaches that compress raw images to decrease the communication. We have also shown that our approach outperforms existing decentralized approaches. Furthermore, we have extended this tracking framework and proposed a sparsitydriven approach for human tracking in VSNs. We have designed special overcomplete dictionaries that exploit the specific known geometry of the measurement scenario and used these dictionaries for sparse representation of likelihoods. By obtaining dictionaries that match the structure of the likelihood functions, we can represent likelihoods with few coefficients, and thereby decrease the communication in the network. This is the first method in the literature that uses sparse representation to compress likelihood functions and applies this idea for VSNs. We have tested our approach for indoor and outdoor tracking scenarios and demonstrated that our approach can achieve bandwidth reduction better than our feature compression framework. We have also presented that our approach outperforms existing decentralized and distributed approaches