{"paper":{"title":"An asymptotic existence result on compressed sensing matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.OC"],"primary_cat":"math.FA","authors_text":"Darryn Bryant, Padraig \\'O Cath\\'ain","submitted_at":"2014-03-12T04:28:42Z","abstract_excerpt":"For any rational number $h$ and all sufficiently large $n$ we give a deterministic construction for an $n\\times \\lfloor hn\\rfloor$ compressed sensing matrix with $(\\ell_1,t)$-recoverability where $t=O(\\sqrt{n})$. Our method uses pairwise balanced designs and complex Hadamard matrices in the construction of $\\epsilon$-equiangular frames, which we introduce as a generalisation of equiangular tight frames. The method is general and produces good compressed sensing matrices from any appropriately chosen pairwise balanced design. The $(\\ell_1,t)$-recoverability performance is specified as a simple "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2807","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"}