{"paper":{"title":"Towards a better compressed sensing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.OC"],"primary_cat":"cs.IT","authors_text":"Mihailo Stojnic","submitted_at":"2013-06-17T10:31:58Z","abstract_excerpt":"In this paper we look at a well known linear inverse problem that is one of the mathematical cornerstones of the compressed sensing field. In seminal works \\cite{CRT,DOnoho06CS} $\\ell_1$ optimization and its success when used for recovering sparse solutions of linear inverse problems was considered. Moreover, \\cite{CRT,DOnoho06CS} established for the first time in a statistical context that an unknown vector of linear sparsity can be recovered as a known existing solution of an under-determined linear system through $\\ell_1$ optimization. In \\cite{DonohoPol,DonohoUnsigned} (and later in \\cite{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3801","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"}