{"paper":{"title":"Improved Bounds on RIP for Generalized Orthogonal Matching Pursuit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Mrityunjoy Chakraborty, Rajib Lochan Das, Siddhartha Satpathi","submitted_at":"2013-02-03T13:40:49Z","abstract_excerpt":"Generalized Orthogonal Matching Pursuit (gOMP) is a natural extension of OMP algorithm where unlike OMP, it may select $N (\\geq1)$ atoms in each iteration. In this paper, we demonstrate that gOMP can successfully reconstruct a $K$-sparse signal from a compressed measurement $ {\\bf y}={\\bf \\Phi x}$ by $K^{th}$ iteration if the sensing matrix ${\\bf \\Phi}$ satisfies restricted isometry property (RIP) of order $NK$ where $\\delta_{NK} < \\frac {\\sqrt{N}}{\\sqrt{K}+2\\sqrt{N}}$. Our bound offers an improvement over the very recent result shown in \\cite{wang_2012b}. Moreover, we present another bound fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0490","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"}