{"paper":{"title":"Orthogonal Matching Pursuit under the Restricted Isometry Property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Albert Cohen, Ronald DeVore, Wolfgang Dahmen","submitted_at":"2015-06-15T21:29:34Z","abstract_excerpt":"This paper is concerned with the performance of Orthogonal Matching Pursuit (OMP) algorithms applied to a dictionary $\\mathcal{D}$ in a Hilbert space $\\mathcal{H}$. Given an element $f\\in \\mathcal{H}$, OMP generates a sequence of approximations $f_n$, $n=1,2,\\dots$, each of which is a linear combination of $n$ dictionary elements chosen by a greedy criterion. It is studied whether the approximations $f_n$ are in some sense comparable to {\\em best $n$ term approximation} from the dictionary. One important result related to this question is a theorem of Zhang \\cite{TZ} in the context of sparse r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04779","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"}