Theory of compressive sensing via \(\ell_1\)-minimization: a non-RIP analysis and extensions (Q384215)
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scientific article; zbMATH DE number 6233805
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Theory of compressive sensing via \(\ell_1\)-minimization: a non-RIP analysis and extensions |
scientific article; zbMATH DE number 6233805 |
Statements
Theory of compressive sensing via \(\ell_1\)-minimization: a non-RIP analysis and extensions (English)
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27 November 2013
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From the author's abstract: We present an alternative, non-restricted isometry property (RIP) analysis for compressive sensing (CS) via \(\ell_1\)-minimization. Our purpose is three-fold: (a) to introduce an elementary and RIP-free treatment for the basic CS theory; (b) to extend the current recoverability and stability results so that prior knowledge can be utilized to enhance recovery via \(\ell_1\)-minimization; and (c) to substantiate a property called uniform recoverability of \(\ell_1\)-minimization; that is, for almost all random measurement matrices recoverability is asymptotically identical. With the aid of two classic results, the non-RIP approach enables us to quickly derive from scratch all basic results for the extended theory.
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compressive sensing
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\(\ell_1\)-minimization
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recoverability
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stability
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prior information
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uniform recoverability
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non-restricted isometry property
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0.9368448
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0.93117386
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0.91464543
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0.9144161
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0.90672904
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0.90661335
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0.9056495
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0.90544975
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0.90445703
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