{"paper":{"title":"Sparse signal recovery by $\\ell_q$ minimization under restricted isometry property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chao-Bing Song, Shu-Tao Xia","submitted_at":"2013-10-09T09:35:32Z","abstract_excerpt":"In the context of compressed sensing, the nonconvex $\\ell_q$ minimization with $0<q<1$ has been studied in recent years. In this paper, by generalizing the sharp bound for $\\ell_1$ minimization of Cai and Zhang, we show that the condition $\\delta_{(s^q+1)k}<\\dfrac{1}{\\sqrt{s^{q-2}+1}}$ in terms of \\emph{restricted isometry constant (RIC)} can guarantee the exact recovery of $k$-sparse signals in noiseless case and the stable recovery of approximately $k$-sparse signals in noisy case by $\\ell_q$ minimization. This result is more general than the sharp bound for $\\ell_1$ minimization when the or"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2410","kind":"arxiv","version":2},"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"}