Download e-book for kindle: A Mathematical Introduction to Compressive Sensing by Simon Foucart

By Simon Foucart

ISBN-10: 0817649476

ISBN-13: 9780817649470

ISBN-10: 0817649484

ISBN-13: 9780817649487

At the intersection of arithmetic, engineering, and computing device technological know-how sits the thriving box of compressive sensing. in response to the idea that facts acquisition and compression could be played concurrently, compressive sensing unearths functions in imaging, sign processing, and lots of different domain names. within the components of utilized arithmetic, electric engineering, and theoretical computing device technological know-how, an explosion of study job has already the theoretical effects that highlighted the potency of the elemental rules. The based rules at the back of those rules also are of self sustaining curiosity to natural mathematicians.

A Mathematical creation to Compressive Sensing supplies an in depth account of the center conception upon which the sector is construct. With simply average necessities, it's a great textbook for graduate classes in arithmetic, engineering, and laptop technological know-how. It additionally serves as a competent source for practitioners and researchers in those disciplines who are looking to gather a cautious knowing of the topic. A Mathematical creation to Compressive Sensing makes use of a mathematical point of view to provide the middle of the speculation underlying compressive sensing.

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Additional resources for A Mathematical Introduction to Compressive Sensing

Sample text

9) in [98] and realized that methods of compressive sensing (the restricted isometry property) are useful for the analysis of sparse regression methods. We refer to [48] and the monograph [76] for details. For more information on machine learning, we direct the reader to [18, 133, 134, 444]. Connections between sparsity and machine learning can be found, for instance, in [23, 147, 513]. Low-rank matrix recovery. The extension of compressive sensing to the recovery of low-rank matrices from incomplete information emerged with the papers [90, 99, 418].

Although certainly interesting, we will not treat low-rank recovery extensively in this book. Nevertheless, due to the close analogy with sparse recovery, the main results are covered in exercises, and the reader is invited to work through them. 3 Overview of the Book Before studying the standard compressive sensing problem on a technical level, it is beneficial to draw a road map of the basic results and solving strategies presented in this book. As previously revealed, the notions of sparsity and compressibility are at the core of compressive sensing.

The theory currently available predicts that sampling sets K chosen uniformly at random among all possible sets of cardinality m work well (at least when W is the identity matrix). Indeed, the results of Chap. 12 guarantee that an s-sparse x ∈ CN can be reconstructed by 1 -minimization if m ≥ Cs ln N . Unfortunately, such random sets K are difficult to realize in practice due to the continuity constraints of the trajectories curves k1 , . . , kL . Therefore, good realizable sets K are investigated empirically.

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A Mathematical Introduction to Compressive Sensing by Simon Foucart


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