- On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using Lq Quasi Norms Hsia Yong(dearyxiagmail.com) Sheu Ruey-Lin(rsheumail.ncku.edu.tw) Abstract: 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. Keywords: compressed sensing, restricted isometry constant, lq minimization, quasi norm Category 1: Applications -- Science and Engineering (Basic Sciences Applications ) Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 3: Global Optimization (Theory ) Citation: unpublished Download: [PDF]Entry Submitted: 09/19/2012Entry Accepted: 09/19/2012Entry Last Modified: 09/19/2012Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.