This textbook introduces sparse and redundant representations with a focus on applications in signal and image processing. The theoretical and numerical foundations are tackled before the applications are discussed. Mathematical modeling for signal sources is discussed along with how to use the proper model for tasks such as denoising, restoration, separation, interpolation and extrapolation, compression, sampling, analysis and synthesis, detection, recognition, and more. The presentation is elegant and engaging. Sparse and Redundant Representations is intended for graduate students in applied mathematics and electrical engineering, as well as applied mathematicians, engineers, and researchers who are active in the fields of signal and image processing.
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From the reviews: “This book approaches sparse and redundant representations from an engineering perspective and emphasizes their use as a signal modeling tool and their application in image and signal processing. … This book is well suited to practitioners in the signals and image processing community … . The public availability of the source code used in the numerical experiments throughout the book could help students make the transition from theory to practice and allow them to get hands-on experience with the inner workings of the various algorithms.” (Ewout van den Berg, SIAM Review, Vol. 53 (4), 2011) “The concept of sparse representations for signals and images is explored in the book under review. … The book offers an important and organized view of this field, setting the foundations of the future research. … The presented book is written to serve as the material for an advanced one-semester graduate course for engineering students. It will be of interest for all specialists working in the area of sparse and redundant representations application in signal and image processing.” (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1211, 2011)
From the Back Cover
The field of sparse and redundant representation modeling has gone through a major revolution in the past two decades. This started with a series of algorithms for approximating the sparsest solutions of linear systems of equations, later to be followed by surprising theoretical results that guarantee these algorithms’ performance. With these contributions in place, major barriers in making this model practical and applicable were removed, and sparsity and redundancy became central, leading to state-of-the-art results in various disciplines. One of the main beneficiaries of this progress is the field of image processing, where this model has been shown to lead to unprecedented performance in various applications. This book provides a comprehensive view of the topic of sparse and redundant representation modeling, and its use in signal and image processing. It offers a systematic and ordered exposure to the theoretical foundations of this data model, the numerical aspects of the involved algorithms, and the signal and image processing applications that benefit from these advancements. The book is well-written, presenting clearly the flow of the ideas that brought this field of research to its current achievements. It avoids a succession of theorems and proofs by providing an informal description of the analysis goals and building this way the path to the proofs. The applications described help the reader to better understand advanced and up-to-date concepts in signal and image processing. Written as a text-book for a graduate course for engineering students, this book can also be used as an easy entry point for readers interested in stepping into this field, and for others already active in this area that are interested in expanding their understanding and knowledge. The book is accompanied by a Matlab software package that reproduces most of the results demonstrated in the book. A link to the free software is available on springer.com.
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7 of 8 people found the following review helpful
By Manchor Ko
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The book starts with a prologue of an under-determined linear system and how sparsity constraints help to solve it with the use of a Langrangian. Next the authors introduce the key idea of how certain norms promote sparsity. There are some good diagrams that really help the geometric intuition (though not as good as the ones by Donoho et al. in connection with Lasso). I really love the way they motivate and frame the entire field but still appeal to concept that most people who have studied linear algebra can relate to.
The first 6 chapters are a master piece in pedagogy. Except for the not so-standard usage of Spark as the measurement of coherence among elements of a dictionary. Mutual coherence is common and easier to grasp since it directly address the size of inner products. This leads to a rather jarring switch when RIP is introduced.
I am still puzzled why the authors do not appeal to frame theory. That leads to strange looking reference to self-dual frames and tight frames when the book never talked about frames.
I also wonder why the authors did not cite Boyd's great book. The treatment of log-barrier was sort of just another penalty function. The term log-barrier was never used in the book.
Overall I cannot put the book down and was especially grateful to the authors for introducing iterative shrinkage as a central theme to link many modern numerical algorithms to solve the basic sparse optimization problem.
The first 6 chapters are a master piece in pedagogy. Except for the not so-standard usage of Spark as the measurement of coherence among elements of a dictionary. Mutual coherence is common and easier to grasp since it directly address the size of inner products. This leads to a rather jarring switch when RIP is introduced.
I am still puzzled why the authors do not appeal to frame theory. That leads to strange looking reference to self-dual frames and tight frames when the book never talked about frames.
I also wonder why the authors did not cite Boyd's great book. The treatment of log-barrier was sort of just another penalty function. The term log-barrier was never used in the book.
Overall I cannot put the book down and was especially grateful to the authors for introducing iterative shrinkage as a central theme to link many modern numerical algorithms to solve the basic sparse optimization problem.
3 of 4 people found the following review helpful
By the27th
Covers the essentials of sparse approximation in a clear and practical style. The sections on basis and matching pursuit algorithms are especially good. There aren't many textbooks on this material and this (with Mallat's "A Wavelet Tour of Signal Processing") is very valuable to mathematicians/engineers/computer scientists working in compressed sensing.
By jjnbos
Amazon Verified Purchase
I'm a Math and Physics PhD from UCSD and I find this too much math and too little signal processing. Might not be a fair criticism but I didn't need to see a lot of proofs that IMHO are too brief to easily follow and too long to be interesting. If I was going to "fix" this, I'd skip the proofs and show a lot of toy examples for the algorithms: you know a 2x 5 matrix with small integers run for a few iterations. As it is too much theory to be practical, too much algo for a math book and so on...
0 of 1 people found the following review helpful
this book is very good. It contain some useful examples and provide software so as to implement most of methods in it.
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