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Journal Articles Studia Mathematica Year : 2010

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.

Dates and versions

hal-00767062 , version 1 (19-12-2012)

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