{"paper":{"title":"Deterministic Bounds for Restricted Isometry of Compressed Sensing Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Richard G. Baraniuk, Shriram Sarvotham","submitted_at":"2011-03-16T23:28:48Z","abstract_excerpt":"Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal $x \\in {\\mathbb R} ^n$ that has only $k \\ll n$ non-zero coefficients from a small number $m \\ll n$ of linear projections. The projections are obtained by multiplying $x$ by a matrix $\\Phi \\in {\\mathbb R}^{m \\times n}$ --- called a CS matrix --- where $k < m \\ll n$. In this work, we ask the following question: given the triplet $\\{k, m, n \\}$ that defines the CS problem size, what are the deterministic limits on the performance of the best CS matrix in ${\\mathbb R}^{m \\times n}$? We select Restricted Iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3316","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"}