{"paper":{"title":"Recovery of Sparse Signals via Generalized Orthogonal Matching Pursuit: A New Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Byonghyo Shim, Jian Wang, Ping Li, Suhyuk Kwon","submitted_at":"2013-04-03T12:51:15Z","abstract_excerpt":"As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using restricted isometry property (RIP). We show that if the measurement matrix $\\mathbf{\\Phi} \\in \\mathcal{R}^{m \\times n}$ satisfies the RIP with $$\\delta_{\\max \\left\\{9, S + 1 \\right\\}K} \\leq \\frac{1}{8},$$ then gOMP performs stable reconstruction of all $K$-sparse signals $\\mathbf{x} \\in \\mathcal{R}^n$ from the noisy measurements $\\mathbf{y} = \\mathbf{\\Ph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0941","kind":"arxiv","version":3},"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"}