Download e-book for iPad: Compressed Sensing : Theory and Applications by Yonina C. Eldar, Gitta Kutyniok

By Yonina C. Eldar, Gitta Kutyniok

ISBN-10: 1107005582

ISBN-13: 9781107005587

ISBN-10: 1139336673

ISBN-13: 9781139336673

Compressed sensing is an exhilarating, speedily growing to be box, attracting massive awareness in electric engineering, utilized arithmetic, records and desktop technological know-how. This booklet offers the 1st precise creation to the topic, highlighting fresh theoretical advances and a variety of purposes, in addition to outlining a variety of final learn demanding situations. After an intensive evaluation of the elemental thought, many state-of-the-art concepts are awarded, together with complicated sign modeling, sub-Nyquist sampling of analog indications, non-asymptotic research of random matrices, adaptive sensing, grasping algorithms and use of graphical types. All chapters are written by means of major researchers within the box, and constant sort and notation are applied all through. Key history details and transparent definitions make this an amazing source for researchers, graduate scholars and practitioners desirous to sign up for this intriguing learn quarter. it could additionally function a supplementary textbook for classes on machine imaginative and prescient, coding concept, sign processing, photo processing and algorithms for effective facts processing.

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Extra info for Compressed Sensing : Theory and Applications

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Specifically, it is shown in [156] that if we are given a point cloud with p points and wish to embed these points in Rm such that the squared 2 distance between any pair of points is preserved up to a factor of 1 ± , then we must have that c0 log(p) m≥ 2 , where c0 > 0 is a constant. The Johnson-Lindenstrauss lemma is closely related to the RIP. In [5] it is shown that any procedure that can be used for generating a linear, distance-preserving embedding for a point cloud can also be used to construct a matrix that satisfies the RIP.

When the measurements are contaminated with noise or have been corrupted by some error such as quantization, it will be useful to consider somewhat stronger conditions. In [43], Candès and Tao introduced the following isometry condition on matrices A and established its important role in CS. 7) holds for all x ∈ Σk . 7) as saying that A approximately preserves the distance between any pair of k-sparse vectors. This will clearly have fundamental implications concerning robustness to noise. Moreover, the potential applications of such stable embeddings range far beyond acquisition for the sole purpose of signal recovery.

D. N (0, σ 2 ). 12) obeys x−x √ 2≤4 2 √ 1 + δ2k √ 1 − (1 + 2)δ2k k log nσ with probability at least 1 − n1 . Ignoring the precise constants and the probabilities with which the stated bounds hold (which we have made no effort to optimize), we observe that in the case when m = O(k log n) these results appear to be essentially the same. However, there is a subtle difference. 1 does not improve as k is reduced. Thus, while they provide very similar guarantees, there are certain circumstances where the Dantzig selector is preferable.

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Compressed Sensing : Theory and Applications by Yonina C. Eldar, Gitta Kutyniok

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