{"paper":{"title":"Restricted $p$-isometry property and its application for nonconvex compressive sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Song Li, Yi Shen","submitted_at":"2010-07-26T08:25:15Z","abstract_excerpt":"Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \\cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers sparse signals from fewer linear measurements than does the $l_1$ minimization. They proved that $l_p$ minimization with $0<p<1$ recovers $S$-sparse signals $x\\in\\RN$ from fewer Gaussian random measurements for some smaller $p$ with probability exceeding $$1 - 1 / {N\\choose S}.$$ The first aim of this paper is to show that above result is right for the case of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4396","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"}