{"paper":{"title":"Expander $\\ell_0$-Decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"math.NA","authors_text":"Jared Tanner, Rodrigo Mendoza-Smith","submitted_at":"2015-08-06T01:37:46Z","abstract_excerpt":"We introduce two new algorithms, Serial-$\\ell_0$ and Parallel-$\\ell_0$ for solving a large underdetermined linear system of equations $y = Ax \\in \\mathbb{R}^m$ when it is known that $x \\in \\mathbb{R}^n$ has at most $k < m$ nonzero entries and that $A$ is the adjacency matrix of an unbalanced left $d$-regular expander graph. The matrices in this class are sparse and allow a highly efficient implementation. A number of algorithms have been designed to work exclusively under this setting, composing the branch of combinatorial compressed-sensing (CCS).\n  Serial-$\\ell_0$ and Parallel-$\\ell_0$ itera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01256","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"}