Ebook: Compressed Sensing & Sparse Filtering

This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary.

Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems.

This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.

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This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary.

Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems.

This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.

---

This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary.

Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems.

This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.

Content:
Front Matter....Pages i-xii
Introduction to Compressed Sensing and Sparse Filtering....Pages 1-23
The Geometry of Compressed Sensing....Pages 25-75
Sparse Signal Recovery with Exponential-Family Noise....Pages 77-93
Nuclear Norm Optimization and Its Application to Observation Model Specification....Pages 95-122
Nonnegative Tensor Decomposition....Pages 123-148
Sub-Nyquist Sampling and Compressed Sensing in Cognitive Radio Networks....Pages 149-185
Sparse Nonlinear MIMO Filtering and Identification....Pages 187-235
Optimization Viewpoint on Kalman Smoothing with Applications to Robust and Sparse Estimation....Pages 237-280
Compressive System Identification....Pages 281-324
Distributed Approximation and Tracking Using Selective Gossip....Pages 325-355
Recursive Reconstruction of Sparse Signal Sequences....Pages 357-380
Estimation of Time-Varying Sparse Signals in Sensor Networks....Pages 381-393
Sparsity and Compressed Sensing in Mono-Static and Multi-Static Radar Imaging....Pages 395-421
Structured Sparse Bayesian Modelling for Audio Restoration....Pages 423-453
Sparse Representations for Speech Recognition....Pages 455-502