{"paper":{"title":"Sparsest Error Detection via Sparsity Invariant Transformation based $\\ell_1$ Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"stat.ME","authors_text":"Sheng Han, Suzhen Wang, Wing Shing Wong, Zhiguo Zhang","submitted_at":"2015-05-20T09:09:32Z","abstract_excerpt":"This paper presents a new method, referred to here as the sparsity invariant transformation based $\\ell_1$ minimization, to solve the $\\ell_0$ minimization problem for an over-determined linear system corrupted by additive sparse errors with arbitrary intensity. Many previous works have shown that $\\ell_1$ minimization can be applied to realize sparse error detection in many over-determined linear systems. However, performance of this approach is strongly dependent on the structure of the measurement matrix, which limits application possibility in practical problems. Here, we present a new app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05290","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"}