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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 Cand`es and Tao, geometric covering arguments of Rudelson and Vershynin, and convex polytopes formulations of Donoho.
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Submitted on : Friday, March 20, 2009 - 3:16:13 PM
Last modification on : Wednesday, November 24, 2021 - 9:54:07 AM
Long-term archiving on: : Thursday, June 10, 2010 - 5:50:45 PM


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  • HAL Id : inria-00369631, version 1



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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