{"paper":{"title":"A study of the universal threshold in the L1 recovery by statistical mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","cond-mat.stat-mech","math.IT"],"primary_cat":"cs.IT","authors_text":"Koujin Takeda, Yoshiyuki Kabashima","submitted_at":"2012-03-28T12:25:42Z","abstract_excerpt":"We discuss the universality of the L1 recovery threshold in compressed sensing. Previous studies in the fields of statistical mechanics and random matrix integration have shown that L1 recovery under a random matrix with orthogonal symmetry has a universal threshold. This indicates that the threshold of L1 recovery under a non-orthogonal random matrix differs from the universal one. Taking this into account, we use a simple random matrix without orthogonal symmetry, where the random entries are not independent, and show analytically that the threshold of L1 recovery for such a matrix does not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6246","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"}