{"paper":{"title":"Exact recoverability from dense corrupted observations via $L_1$ minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Nam H. Nguyen, Trac. D. Tran","submitted_at":"2011-02-07T03:57:26Z","abstract_excerpt":"This paper confirms a surprising phenomenon first observed by Wright \\textit{et al.} \\cite{WYGSM_Face_2009_J} \\cite{WM_denseError_2010_J} under different setting: given $m$ highly corrupted measurements $y = A_{\\Omega \\bullet} x^{\\star} + e^{\\star}$, where $A_{\\Omega \\bullet}$ is a submatrix whose rows are selected uniformly at random from rows of an orthogonal matrix $A$ and $e^{\\star}$ is an unknown sparse error vector whose nonzero entries may be unbounded, we show that with high probability $\\ell_1$-minimization can recover the sparse signal of interest $x^{\\star}$ exactly from only $m = C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1227","kind":"arxiv","version":3},"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"}