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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.

《Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries》文章matlab代码实现

Compressed-Sensing is a recent branch that separated from sparse and redundant representations, becoming a center of interest of its own. Exploiting sparse representation of signals, their sampling can be made far more eective compared to the classical Nyquist-Shannon sampling. In a recent work that emerged in 2006 by Emmanuel Candes, Justin Romberg, Terence Tao, David Donoho, and others that followed, the theory and practice of this field were beautifully formed, sweeping many researchers and practitioners in excitement. The impact this field has is immense, strengthened by the warm hug by information-theorists, leading mathematicians, and others. So popular has this field become that many confuse it with being the complete story of sparse representation modeling. In this book I discuss the branch of activity on Compressed-Sensing very briefly, and mostly so as to tie it to the more general results known in sparse representation theory. I believe that the accumulated knowledge on compressed-sensing could easily fill a separate book.

Sparse and Redundant Representations：From Theory to Applications in Signal and Image Processing。以色列理工大学Michael Elad写的书，非常好。《稀疏与冗余表示-理论及其在信号与图像处理中的应》

From Theory to Applications in Signal and Image Processing

Sparse+and+Redundant+Representation一书的matlab-code

本书主要描述了基于压缩感知的理论，恢复算法，还有详细介绍了应用，特别适合学习压缩感知的人使用

这是一本关于稀疏表达在信号和图像处理中运用的权威书籍《Sparse and Redundant Representations From Theory to Applications in Signal and Image Processing》，也是第一部关于稀疏表达的书籍。是稀疏表达的大牛Michael Elad编写的。现在在卓越上有的卖，不过要7百多元，太贵，还是搞电子版看实惠点。

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. * Introduces theoretical and numerical foundations before tackling applications * Discusses how to use the proper model for various situations * Introduces sparse and redundant representations * Focuses on applications in signal and image processing 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 aspec