{"paper":{"title":"Sharp Sufficient Conditions for Stable Recovery of Block Sparse Signals by Block Orthogonal Matching Pursuit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jinming Wen, Ming-Jun Lai, Xiaohu Tang, Zhengchun Zhou, Zilong Liu","submitted_at":"2016-05-10T09:03:30Z","abstract_excerpt":"In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm to recover block sparse signals $\\x$ from measurements $\\y=\\A\\x+\\v$, where $\\v$ is an $\\ell_2$-bounded noise vector (i.e., $\\|\\v\\|_2\\leq \\epsilon$ for some constant $\\epsilon$). We investigate some sufficient conditions based on the block restricted isometry property (block-RIP) for exact (when $\\v=\\0$) and stable (when $\\v\\neq\\0$) recovery of block sparse signals $\\x$. First, on the one hand, we show that if $\\A$ satisfies the block-RIP with $\\delta_{K+1}<1/\\sqrt{K+1}$, then every block $K$-sparse signal $\\x$ can be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02894","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"}