{"paper":{"title":"A remark on the Restricted Isometry Property in Orthogonal Matching Pursuit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Qun Mo, Yi Shen","submitted_at":"2012-01-13T02:47:59Z","abstract_excerpt":"This paper demonstrates that if the restricted isometry constant $\\delta_{K+1}$ of the measurement matrix $A$ satisfies $$ \\delta_{K+1} < \\frac{1}{\\sqrt{K}+1}, $$ then a greedy algorithm called Orthogonal Matching Pursuit (OMP) can recover every $K$--sparse signal $\\mathbf{x}$ in $K$ iterations from $A\\x$. By contrast, a matrix is also constructed with the restricted isometry constant $$ \\delta_{K+1} = \\frac{1}{\\sqrt{K}} $$ such that OMP can not recover some $K$-sparse signal $\\mathbf{x}$ in $K$ iterations. This result positively verifies the conjecture given by Dai and Milenkovic in 2009."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.2733","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"}