Average Reviews:
(More customer reviews)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.
Click Here to see more reviews about: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing
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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