{"paper":{"title":"Compressed sensing with sparse, structured matrices","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":"Federico Ricci-Tersenghi, Maria Chiara Angelini, Yoshiyuki Kabashima","submitted_at":"2012-07-12T06:16:33Z","abstract_excerpt":"In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the original signal, compressed at a rate {\\alpha}, by using a message passing algorithm (Expectation Maximization Belief Propagation) that runs in a time linear in N. In the large N limit, the scheme proposed here closely approaches the theoretical bound {\\rho}0 = {\\alpha}, and so it is both optimal and efficient (linear time complexity). More generally, we show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2853","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"}