Adaptive Methods and Theory for Sparse Signal Recovery - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Methods and Theory for Sparse Signal Recovery write by . This book was released on 2012. Adaptive Methods and Theory for Sparse Signal Recovery available in PDF, EPUB and Kindle. The study of sparsity has recently been given tremendous attention within the signal processing community. Sparsity is the simple notion that a high dimensional signal or vector can be well represented by a relatively small number of coefficients; sparse signals arise in communications, coding, remote sensing, imaging, biology, medicine, and many more. Adaptivity, the ability to change behavior based on input from the environment, has long been recognized by engineers as a means to improve performance. The focus of this thesis is development of adaptive measurement techniques and theory for sparse signal recovery problems. Surprisingly, adaptive measurement systems can drastically improve performance by reducing the signal noise ratio (SNR) needed for successful inference of a sparse signal. The first portion of this thesis comprises contributions to the study of multiple-testing and sparse recovery problems from the perspective of sequential analysis. We propose a simple yet powerful adaptive procedure termed Sequential Thresholding, which can succeed with a relatively small number of adaptive measurements. We develop the fundamental performance limits of adaptive testing in this setting, and prove the asymptotic optimality of Sequential Thresholding. We then transition to the field of compressive sensing. In this setting we develop an adaptive, compressive, search procedure that is provably optimal in terms of dependence on SNR for a certain class of sparse signals. The fourth chapter of this thesis focuses on a problem termed the search across multiple populations. Here, sparsity manifests itself as the rare occurrence of some `atypical' statistical population. A general theory is developed, with tight upper and lower bounds on the number of samples required to find such an atypical population. Instantiating the general theory results in the tightest known bounds for some well-studied problems. Lastly, this thesis focuses on the problem of non-coherent signal detection in multipath fading channels. Here, the signaling duration and bandwidth of the transmit signal are adapted to exploit the statistical behavior of the wireless environment. Sparsity arises as bandwidth and signaling duration become large.
Dynamic Compressive Sensing
Dynamic Compressive Sensing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dynamic Compressive Sensing write by Muhammad Salman Asif. This book was released on 2013. Dynamic Compressive Sensing available in PDF, EPUB and Kindle. This thesis presents compressive sensing algorithms that utilize system dynamics in the sparse signal recovery process. These dynamics may arise due to a time-varying signal, streaming measurements, or an adaptive signal transform. Compressive sensing theory has shown that under certain conditions, a sparse signal can be recovered from a small number of linear, incoherent measurements. The recovery algorithms, however, for the most part are static: they focus on finding the solution for a fixed set of measurements, assuming a fixed (sparse) structure of the signal. In this thesis, we present a suite of sparse recovery algorithms that cater to various dynamical settings. The main contributions of this research can be classified into the following two categories: 1) Efficient algorithms for fast updating of L1-norm minimization problems in dynamical settings. 2) Efficient modeling of the signal dynamics to improve the reconstruction quality; in particular, we use inter-frame motion in videos to improve their reconstruction from compressed measurements. Dynamic L1 updating: We present homotopy-based algorithms for quickly updating the solution for various L1 problems whenever the system changes slightly. Our objective is to avoid solving an L1-norm minimization program from scratch; instead, we use information from an already solved L1 problem to quickly update the solution for a modified system. Our proposed updating schemes can incorporate time-varying signals, streaming measurements, iterative reweighting, and data-adaptive transforms. Classical signal processing methods, such as recursive least squares and the Kalman filters provide solutions for similar problems in the least squares framework, where each solution update requires a simple low-rank update. We use homotopy continuation for updating L1 problems, which requires a series of rank-one updates along the so-called homotopy path. Dynamic models in video: We present a compressive-sensing based framework for the recovery of a video sequence from incomplete, non-adaptive measurements. We use a linear dynamical system to describe the measurements and the temporal variations of the video sequence, where adjacent images are related to each other via inter-frame motion. Our goal is to recover a quality video sequence from the available set of compressed measurements, for which we exploit the spatial structure using sparse representations of individual images in a spatial transform and the temporal structure, exhibited by dependencies among neighboring images, using inter-frame motion. We discuss two problems in this work: low-complexity video compression and accelerated dynamic MRI. Even though the processes for recording compressed measurements are quite different in these two problems, the procedure for reconstructing the videos is very similar.
Adaptive Signal Processing
Adaptive Signal Processing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Signal Processing write by Tülay Adali. This book was released on 2010-06-25. Adaptive Signal Processing available in PDF, EPUB and Kindle. Leading experts present the latest research results in adaptive signal processing Recent developments in signal processing have made it clear that significant performance gains can be achieved beyond those achievable using standard adaptive filtering approaches. Adaptive Signal Processing presents the next generation of algorithms that will produce these desired results, with an emphasis on important applications and theoretical advancements. This highly unique resource brings together leading authorities in the field writing on the key topics of significance, each at the cutting edge of its own area of specialty. It begins by addressing the problem of optimization in the complex domain, fully developing a framework that enables taking full advantage of the power of complex-valued processing. Then, the challenges of multichannel processing of complex-valued signals are explored. This comprehensive volume goes on to cover Turbo processing, tracking in the subspace domain, nonlinear sequential state estimation, and speech-bandwidth extension. Examines the seven most important topics in adaptive filtering that will define the next-generation adaptive filtering solutions Introduces the powerful adaptive signal processing methods developed within the last ten years to account for the characteristics of real-life data: non-Gaussianity, non-circularity, non-stationarity, and non-linearity Features self-contained chapters, numerous examples to clarify concepts, and end-of-chapter problems to reinforce understanding of the material Contains contributions from acknowledged leaders in the field Adaptive Signal Processing is an invaluable tool for graduate students, researchers, and practitioners working in the areas of signal processing, communications, controls, radar, sonar, and biomedical engineering.
Nonuniform Sampling
Nonuniform Sampling - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonuniform Sampling write by Farokh Marvasti. This book was released on 2012-12-06. Nonuniform Sampling available in PDF, EPUB and Kindle. Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated. History is a collection of important events that are nonuniformly spaced in time. Historians infer between events (interpolation) and politicians and stock market analysts forecast the future from past and present events (extrapolation). The 20 chapters of Nonuniform Sampling: Theory and Practice contain contributions by leading researchers in nonuniform and Shannon sampling, zero crossing, and interpolation theory. Its practical applications include NMR, seismology, speech and image coding, modulation and coding, optimal content, array processing, and digital filter design. It has a tutorial outlook for practising engineers and advanced students in science, engineering, and mathematics. It is also a useful reference for scientists and engineers working in the areas of medical imaging, geophysics, astronomy, biomedical engineering, computer graphics, digital filter design, speech and video processing, and phased array radar.
Sparse Optimization Theory and Methods
Sparse Optimization Theory and Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sparse Optimization Theory and Methods write by Yun-Bin Zhao. This book was released on 2018-07-04. Sparse Optimization Theory and Methods available in PDF, EPUB and Kindle. Seeking sparse solutions of underdetermined linear systems is required in many areas of engineering and science such as signal and image processing. The efficient sparse representation becomes central in various big or high-dimensional data processing, yielding fruitful theoretical and realistic results in these fields. The mathematical optimization plays a fundamentally important role in the development of these results and acts as the mainstream numerical algorithms for the sparsity-seeking problems arising from big-data processing, compressed sensing, statistical learning, computer vision, and so on. This has attracted the interest of many researchers at the interface of engineering, mathematics and computer science. Sparse Optimization Theory and Methods presents the state of the art in theory and algorithms for signal recovery under the sparsity assumption. The up-to-date uniqueness conditions for the sparsest solution of underdertemined linear systems are described. The results for sparse signal recovery under the matrix property called range space property (RSP) are introduced, which is a deep and mild condition for the sparse signal to be recovered by convex optimization methods. This framework is generalized to 1-bit compressed sensing, leading to a novel sign recovery theory in this area. Two efficient sparsity-seeking algorithms, reweighted l1-minimization in primal space and the algorithm based on complementary slackness property, are presented. The theoretical efficiency of these algorithms is rigorously analysed in this book. Under the RSP assumption, the author also provides a novel and unified stability analysis for several popular optimization methods for sparse signal recovery, including l1-mininization, Dantzig selector and LASSO. This book incorporates recent development and the author’s latest research in the field that have not appeared in other books.
