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- W4293696423 abstract "This paper follows the recent discussion on the sparse solution recovery with quasi-norms $ell_q,~qin(0,1)$ 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 $l_q$ minimization, at least for those $qin(0,0.9181]$, is the sparse solution of the corresponding underdetermined linear system. Moreover, if $delta_{2k}le0.4931$, the sparse solution can be recovered by any $l_q, qin(0,1)$ minimization. The values $0.9181$ and $0.4931$ improves those reported previously in the literature." @default.
- W4293696423 created "2022-08-31" @default.
- W4293696423 creator A5005789866 @default.
- W4293696423 creator A5013665956 @default.
- W4293696423 date "2013-12-11" @default.
- W4293696423 modified "2023-09-23" @default.
- W4293696423 title "On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using $ell_q$ Quasi Norms" @default.
- W4293696423 doi "https://doi.org/10.48550/arxiv.1312.3379" @default.
- W4293696423 hasPublicationYear "2013" @default.
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