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Sparse recovery with pre-Gaussian random matrices

Abstract : For an m×N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ1-minimization under the optimal condition m≥csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ1-norm and the outer norm depends on probability distributions.
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https://hal.inria.fr/hal-00767062
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Submitted on : Wednesday, December 19, 2012 - 2:18:26 PM
Last modification on : Saturday, June 19, 2021 - 3:50:41 AM

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Simon Foucart, Ming-Jun Lai. Sparse recovery with pre-Gaussian random matrices. Studia Mathematica, Instytut Matematyczny - Polska Akademii Nauk, 2010, 200, pp.91--102. ⟨10.4064/sm200-1-6⟩. ⟨hal-00767062⟩

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