# Phase Transitions for Restricted Isometry Properties

Abstract : Currently there is no framework for the transparent comparison of sparse approximation recoverability results derived using different methods of analysis. We cast some of the most recent recoverability results for 1-regularization in terms of the phase transition framework advocated by Donoho. To allow for quantitative comparisons across different methods of analysis a particular random matrix ensemble must be selected; here we focus on Gaussian random matrices. Methods of analysis considered include the Restricted Isometry Property of Candes and Tao, geometric covering arguments of Rudelson and Vershynin, and convex polytopes formulations of Donoho.
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Conference papers
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Cited literature [11 references]

https://hal.inria.fr/inria-00369631
Contributor : Ist Rennes <>
Submitted on : Friday, March 20, 2009 - 3:16:13 PM
Last modification on : Thursday, October 26, 2017 - 4:34:02 PM
Long-term archiving on: : Thursday, June 10, 2010 - 5:50:45 PM

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• HAL Id : inria-00369631, version 1

### Citation

Jeffrey D. Blanchard, Coralia Cartis, Jared Tanner. Phase Transitions for Restricted Isometry Properties. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369631⟩

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