Sparse and Redundant Representations

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.