{"paper":{"title":"Stable Recovery of Sparse Signals via $l_p-$Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Dongfang Li, Fumin Zhu, Jinming Wen","submitted_at":"2014-06-17T11:42:42Z","abstract_excerpt":"In this paper, we show that, under the assumption that $\\|\\e\\|_2\\leq \\epsilon$, every $k-$sparse signal $\\x\\in \\mathbb{R}^n$ can be stably ($\\epsilon\\neq0$) or exactly recovered ($\\epsilon=0$) from $\\y=\\A\\x+\\e$ via $l_p-$mnimization with $p\\in(0, \\bar{p}]$, where \\beqnn \\bar{p}= \\begin{cases} \\frac{50}{31}(1-\\delta_{2k}), &\\delta_{2k}\\in[\\frac{\\sqrt{2}}{2}, 0.7183)\\cr 0.4541, &\\delta_{2k}\\in[0.7183,0.7729)\\cr 2(1-\\delta_{2k}), &\\delta_{2k}\\in[0.7729,1) \\end{cases}, \\eeqnn even if the restricted isometry constant of $\\A$ satisfies $\\delta_{2k}\\in[\\frac{\\sqrt{2}}{2}, 1)$. Furthermore, under the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4328","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"}