{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4MS2SE7YYCTHWFKGVWPFLSL2OK","short_pith_number":"pith:4MS2SE7Y","schema_version":"1.0","canonical_sha256":"e325a913f8c0a67b1546ad9e55c97a72a2f7b0b1adbcc7a8a04f4ca34773d377","source":{"kind":"arxiv","id":"1501.04817","version":1},"attestation_state":"computed","paper":{"title":"Support Recovery with Orthogonal Matching Pursuit in the Presence of Noise: A New Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jian Wang","submitted_at":"2015-01-20T14:20:43Z","abstract_excerpt":"Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We consider two signal-to-noise ratio (SNR) settings: i) the SNR depends on the sparsity level $K$ of input signals, and ii) the SNR is an absolute constant independent of $K$. For the first setting, we establish necessary and sufficient conditions for the exact support recovery with OMP, expressed as lower bounds on the SNR. Our results indicate that in order "},"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":"1501.04817","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-20T14:20:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"7f766a90f231c5ac056610d6a587fda7d29019385bd2f11769990e68b4b98967","abstract_canon_sha256":"42460b206511e1e32b6b7de09aec18f521effe214ab77a94a9410bacb1391bae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:03.811310Z","signature_b64":"lagO7GB2NQmK4PHBbIbPNTzHsPdphahrFxlgQQXc4WPKa7cQVzln5ZRtHpdU2uq91+q51cuEFYkgtC1Vx5GnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e325a913f8c0a67b1546ad9e55c97a72a2f7b0b1adbcc7a8a04f4ca34773d377","last_reissued_at":"2026-05-18T01:29:03.810582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:03.810582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Support Recovery with Orthogonal Matching Pursuit in the Presence of Noise: A New Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jian Wang","submitted_at":"2015-01-20T14:20:43Z","abstract_excerpt":"Support recovery of sparse signals from compressed linear measurements is a fundamental problem in compressed sensing (CS). In this paper, we study the orthogonal matching pursuit (OMP) algorithm for the recovery of support under noise. We consider two signal-to-noise ratio (SNR) settings: i) the SNR depends on the sparsity level $K$ of input signals, and ii) the SNR is an absolute constant independent of $K$. For the first setting, we establish necessary and sufficient conditions for the exact support recovery with OMP, expressed as lower bounds on the SNR. Our results indicate that in order "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04817","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.04817","created_at":"2026-05-18T01:29:03.810701+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04817v1","created_at":"2026-05-18T01:29:03.810701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04817","created_at":"2026-05-18T01:29:03.810701+00:00"},{"alias_kind":"pith_short_12","alias_value":"4MS2SE7YYCTH","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4MS2SE7YYCTHWFKG","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4MS2SE7Y","created_at":"2026-05-18T12:29:05.191682+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/4MS2SE7YYCTHWFKGVWPFLSL2OK","json":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK.json","graph_json":"https://pith.science/api/pith-number/4MS2SE7YYCTHWFKGVWPFLSL2OK/graph.json","events_json":"https://pith.science/api/pith-number/4MS2SE7YYCTHWFKGVWPFLSL2OK/events.json","paper":"https://pith.science/paper/4MS2SE7Y"},"agent_actions":{"view_html":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK","download_json":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK.json","view_paper":"https://pith.science/paper/4MS2SE7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04817&json=true","fetch_graph":"https://pith.science/api/pith-number/4MS2SE7YYCTHWFKGVWPFLSL2OK/graph.json","fetch_events":"https://pith.science/api/pith-number/4MS2SE7YYCTHWFKGVWPFLSL2OK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK/action/storage_attestation","attest_author":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK/action/author_attestation","sign_citation":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK/action/citation_signature","submit_replication":"https://pith.science/pith/4MS2SE7YYCTHWFKGVWPFLSL2OK/action/replication_record"}},"created_at":"2026-05-18T01:29:03.810701+00:00","updated_at":"2026-05-18T01:29:03.810701+00:00"}