{"paper":{"title":"Information-Theoretically Optimal Compressed Sensing via Spatial Coupling and Approximate Message Passing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Adel Javanmard, Andrea Montanari, David L. Donoho","submitted_at":"2011-12-04T01:27:08Z","abstract_excerpt":"We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by Krzakala et al. \\cite{KrzakalaEtAl}, message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements with undersampling rates close to the fraction of non-zero coordinates.\n  We use an approximate message passing (AMP) algorithm and analyze it through the state evolution method. We give a rigorous proof tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0708","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"}