{"paper":{"title":"Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Arye Nehorai, Gongguo Tang","submitted_at":"2010-04-23T20:39:35Z","abstract_excerpt":"The stability of sparse signal reconstruction is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique $\\ell_1$ sparse recovery. One of our algorithm produces comparable results with the state-of-the-art technique and performs orders of magnitude faster. We show that the $\\ell_1$-constrained minimal singular value ($\\ell_1$-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of $\\ell_1$-based algorithms such as the Basis Pursuit, the Dantzig selector, and the LASSO estimator. Compared with performance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.4222","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"}