{"paper":{"title":"New Accumulative Score Function Based Bound For Sparsity Level of L1 Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Sheng Han, Suzhen Wang, Zhiguo Zhang","submitted_at":"2014-10-09T13:20:21Z","abstract_excerpt":"This paper discusses a fundamental problem in compressed sensing: the sparse recoverability of L1 minimization with an arbitrary sensing matrix. We develop an new accumulative score function (ASF) to provide a lower bound for the recoverable sparsity level (SL) of a sensing matrix while preserving a low computational complexity. We first define a score function for each row of a matrix, and then ASF sums up large scores until the total score reaches 0.5. Interestingly, the number of involved rows in the summation is a reliable lower bound of SL. It is further proved that ASF provides a sharper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2447","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"}