{"paper":{"title":"On RIC bounds of Compressed Sensing Matrices for Approximating Sparse Solutions Using $\\ell_q$ Quasi Norms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Ruey-Lin Sheu, Yong Hsia","submitted_at":"2013-12-12T01:16:40Z","abstract_excerpt":"This paper follows the recent discussion on the sparse solution recovery with quasi-norms $\\ell_q,~q\\in(0,1)$ 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 $l_q$ minimization, at least for those $q\\in(0,0.9181]$, is the sparse solution of the corresponding underdetermined linear system. Moreover, if $\\delta_{2k}\\le0.4931$, the sparse solution can be reco"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3379","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}