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 > cs In (e N/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. © Instytut Matematyczny PAN, 2010.