On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using Lq Quasi Norms

This paper follows the recent discussion on the sparse solution recovery with quasi-norms Lq; q\in(0,1) when the sensing matrix possesses a Restricted Isometry Constant \delta_{2k} (RIC). Our key tool is an improvement on a version of the converse of a generalized Cauchy-Schwarz inequality" extended to the setting of quasi-norm. We show that, if \delta_{2k}\le 1/2, any minimizer of the Lq minimization, at least for those q\in (0, 0.9181], is the sparse solution of the corresponding underdetermined linear system. Moreover, if \delta_{2k}\le 0.4931, the sparse solution can be recovered by any lq; q \in(0,1) minimization. The values 0.9181 and 0.4931 improves those reported previously in the literature.

unpublished