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Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing Hardcover – August 19, 2010

ISBN-13: 978-1441970107 ISBN-10: 144197010X Edition: 2010th

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Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing + Sparse Representations and Compressive Sensing for Imaging and Vision (SpringerBriefs in Electrical and Computer Engineering) + Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity
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Product Details

  • Hardcover: 376 pages
  • Publisher: Springer; 2010 edition (August 19, 2010)
  • Language: English
  • ISBN-10: 144197010X
  • ISBN-13: 978-1441970107
  • Product Dimensions: 9.2 x 6.1 x 1 inches
  • Shipping Weight: 1.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (5 customer reviews)
  • Amazon Best Sellers Rank: #412,327 in Books (See Top 100 in Books)

Editorial Reviews

Review

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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Most Helpful Customer Reviews

12 of 13 people found the following review helpful By Manchor Ko on June 2, 2011
Format: Hardcover Verified Purchase
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.
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5 of 6 people found the following review helpful By the27th on May 28, 2011
Format: Hardcover
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.
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3 of 4 people found the following review helpful By Anne van Rossum on June 20, 2013
Format: Hardcover
This book is about sparse representations. Mathematically it is all about solving:

min ||x||_0 subject to Ax=b

where ||x||_0 is a special type of "norm", it counts the nonzero entries in a vector x. And the issue at hand is that only a few columns in A will (multiplied by x) result in b. In other words, in many practical circumstances - apparently - this vector x only requires a few nonzero entries.

I am only on a third or so of the book (after one weekend), so I've to adjust my review later. Until now the authors do focus on trying to get theoretical grips on this topic. When is there a sparse solution? If you have one, can you find an even sparser one. I find many angles very interesting. That an uncertainty principles leads to a uniqueness result is amazing. The authors subsequently introduce the concept of a "spark" and are able to say if for example matching pursuit will succeed in recovering the sparsest solution.

In general the authors are using math all over the place, so if you don't like math stay away from the book. However, they take a very gentle approach from my perspective (as a robotics engineer), making quite some intermediate steps explicit. Of course, I have to go back some pages so now and then, but it's worthwhile. And I look forward to the second part of the book that describes the image processing applications, which after skimming looks much less "math-heavy", but where I hope the authors maintained the same pleasant level of detail.
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2 of 3 people found the following review helpful By jjnbos on May 8, 2013
Format: Hardcover 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...
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2 of 3 people found the following review helpful By changjiang zhang on December 31, 2012
Format: Hardcover
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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