{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NAY3PUWHB3BO66RFBCWKI3RCQW","short_pith_number":"pith:NAY3PUWH","schema_version":"1.0","canonical_sha256":"6831b7d2c70ec2ef7a2508aca46e2285ac5fc3f570559292488cd1f49e529329","source":{"kind":"arxiv","id":"1605.02894","version":2},"attestation_state":"computed","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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.02894","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-05-10T09:03:30Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e518d815b5437253c074f283b8653dd5160428e182e2392de78ccb026381292f","abstract_canon_sha256":"5f337b2990f5dabb30a9dff847c5f6da20668742aedbf53d695f668a77442dbf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:03.348121Z","signature_b64":"J37eEkJhTSY9f0dUE3qvDI42zUhNiH1qPWu2pQfR2tHaC77fC+4BIzf4U2jpbqAJNR85opECFabtBctGMvwRDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6831b7d2c70ec2ef7a2508aca46e2285ac5fc3f570559292488cd1f49e529329","last_reissued_at":"2026-05-18T00:16:03.347647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:03.347647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.02894","created_at":"2026-05-18T00:16:03.347719+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.02894v2","created_at":"2026-05-18T00:16:03.347719+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02894","created_at":"2026-05-18T00:16:03.347719+00:00"},{"alias_kind":"pith_short_12","alias_value":"NAY3PUWHB3BO","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NAY3PUWHB3BO66RF","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NAY3PUWH","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW","json":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW.json","graph_json":"https://pith.science/api/pith-number/NAY3PUWHB3BO66RFBCWKI3RCQW/graph.json","events_json":"https://pith.science/api/pith-number/NAY3PUWHB3BO66RFBCWKI3RCQW/events.json","paper":"https://pith.science/paper/NAY3PUWH"},"agent_actions":{"view_html":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW","download_json":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW.json","view_paper":"https://pith.science/paper/NAY3PUWH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.02894&json=true","fetch_graph":"https://pith.science/api/pith-number/NAY3PUWHB3BO66RFBCWKI3RCQW/graph.json","fetch_events":"https://pith.science/api/pith-number/NAY3PUWHB3BO66RFBCWKI3RCQW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW/action/storage_attestation","attest_author":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW/action/author_attestation","sign_citation":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW/action/citation_signature","submit_replication":"https://pith.science/pith/NAY3PUWHB3BO66RFBCWKI3RCQW/action/replication_record"}},"created_at":"2026-05-18T00:16:03.347719+00:00","updated_at":"2026-05-18T00:16:03.347719+00:00"}