A Mathematical Introduction to Compressive Sensing - download pdf or read online

By Simon Foucart

ISBN-10: 0817649476

ISBN-13: 9780817649470

ISBN-10: 0817649484

ISBN-13: 9780817649487

At the intersection of arithmetic, engineering, and desktop technology sits the thriving box of compressive sensing. in response to the idea that information acquisition and compression should 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 laptop technological know-how, an explosion of analysis job has already the theoretical effects that highlighted the potency of the elemental ideas. The based rules in the back of those rules also are of self sustaining curiosity to natural mathematicians.

A Mathematical advent to Compressive Sensing offers a close account of the middle thought upon which the sector is construct. With in simple terms average necessities, it's a great textbook for graduate classes in arithmetic, engineering, and laptop technology. 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 advent to Compressive Sensing makes use of a mathematical viewpoint to offer the middle of the idea underlying compressive sensing.

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

On the intersection of arithmetic, engineering, and laptop technology sits the thriving box of compressive sensing. in accordance with the idea that info acquisition and compression could be played concurrently, compressive sensing unearths functions in imaging, sign processing, and plenty of different domain names.

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Extra info for A Mathematical Introduction to Compressive Sensing

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The number of samples allowing one to recover a fixed s-sparse coefficient vector x with high probability is then m ≥ CK 2 s ln N . 19) is a highlight of the theory of compressive sensing. It states that δs ≤ δ with high probability provided m ≥ CK 2 δ −2 s ln4 (N ). We close Chap. 12 by illustrating some connections to the Λ1 -problem from harmonic analysis. A further type of measurement matrix used in compressive sensing is considered in Chap. 13. It arises as the adjacency matrix of certain bipartite graphs called lossless expanders.

Taking the sparsity of x into consideration, we arrive at the standard compressive sensing problem. The associated reconstruction algorithms, including 1 -minimization, apply. It remains to find suitable radio pulse sequences g ∈ Cm ensuring that x can be recovered from y = Bg. A popular choice of g is the so-called Alltop vector, which is defined for prime m ≥ 5 as g = e2πi 3 /m , ∈ [m]. We refer to Chap. 5 for more details and to Fig. 8 for a numerical example. Although the Alltop window works well in practice, the theoretical guarantees currently available are somewhat limited due to the fact that g is deterministic.

The corresponding output yj would be another quantity of interest, for instance, the probability that jth patient suffers a certain disease. , to determine the parameter vector x. In practice, the number N of parameters is often much larger than the number m of observations, so even without noise, the problem of fitting the parameter x is illposed without further assumption. In many cases, however, only a small number of parameters contribute towards the effect to be predicted, but it is a priori unknown which of these parameters are influential.

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A Mathematical Introduction to Compressive Sensing by Simon Foucart


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