New York: Springer, 2010. - 397 p. This book was originally written to serve as the material for an advanced one- semester (fourteen 2-hour lectures) graduate course for engineering students at the Technion, Israel. It is originally based on a review paper that I wrote together with Alfred M. Bruckstein and David L. Donoho, which appeared in SIAM Review on February 2009. The content of this paper has been massively modified and extended to become an appropriate material for an advanced graduate course. In this book I introduce the topic of sparse and redundant representations, show the questions posed in this field, and the answers they get, present the flavor of the research in this arena, the people involved, and more. It is my desire to expose the readers of this book (and the students in the course) to the beauty of this field, and the potential it encompasses for various disciplines. So, what is it all about? Mathematicians active in this field (and there are many of those) would mention the deep relation between this emerging field and harmonic analysis, approximation theory, and wavelets, in their answer. However, this is not my answer. As an engineer, my interest is more in the practical sides of this field, and thus my entire motivation for studying sparse and redundant representations comes from the applications they serve in signal and image processing. This is not to say that I find little interest in the theoretical sides of the activity in sparse and redundant representations. However, these theoretical results should be considered in the context of the wider picture.
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