{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:EMKRLC5W63GS6ZNIS2C7QYR7WF","short_pith_number":"pith:EMKRLC5W","schema_version":"1.0","canonical_sha256":"2315158bb6f6cd2f65a89685f8623fb1766c73185270a0b0faf0e453dc20bd95","source":{"kind":"arxiv","id":"1207.1855","version":1},"attestation_state":"computed","paper":{"title":"Recoverability Analysis for Modified Compressive Sensing with Partially Known Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jun Zhang, Yuanqing Li, Zhenghui Gu, Zhu Liang Yu","submitted_at":"2012-07-08T08:58:40Z","abstract_excerpt":"The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on the reliability of the known support. An important problem, which must be studied further, is the recoverability of modified-CS when the known support contains a number of errors. In this letter, we analyze the recoverability of modified-CS in a stochastic framework. A sufficient and necessary condition is established for exact recovery of a sparse signal. Uti"},"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":"1207.1855","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-08T08:58:40Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"cac2ca25723d75e100d8af0e199f4bea89ed2e08493104942ed8f4268135cac4","abstract_canon_sha256":"449c76651cfa38a19cf363ef7f1a9e107292488d061f344d6ce5a4ec87f70a16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:26.731092Z","signature_b64":"CnTafvy6I2Qp/Q0G7SRhPuPKE+atj1QZBGFQgOY2TBiO9adKQ3GAfHddakUB/6Hl5WpSy3yabSYQ3E+GJwzTAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2315158bb6f6cd2f65a89685f8623fb1766c73185270a0b0faf0e453dc20bd95","last_reissued_at":"2026-05-18T03:51:26.730448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:26.730448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recoverability Analysis for Modified Compressive Sensing with Partially Known Support","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jun Zhang, Yuanqing Li, Zhenghui Gu, Zhu Liang Yu","submitted_at":"2012-07-08T08:58:40Z","abstract_excerpt":"The recently proposed modified-compressive sensing (modified-CS), which utilizes the partially known support as prior knowledge, significantly improves the performance of recovering sparse signals. However, modified-CS depends heavily on the reliability of the known support. An important problem, which must be studied further, is the recoverability of modified-CS when the known support contains a number of errors. In this letter, we analyze the recoverability of modified-CS in a stochastic framework. A sufficient and necessary condition is established for exact recovery of a sparse signal. Uti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1855","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":"1207.1855","created_at":"2026-05-18T03:51:26.730551+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.1855v1","created_at":"2026-05-18T03:51:26.730551+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1855","created_at":"2026-05-18T03:51:26.730551+00:00"},{"alias_kind":"pith_short_12","alias_value":"EMKRLC5W63GS","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"EMKRLC5W63GS6ZNI","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"EMKRLC5W","created_at":"2026-05-18T12:27:04.183437+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/EMKRLC5W63GS6ZNIS2C7QYR7WF","json":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF.json","graph_json":"https://pith.science/api/pith-number/EMKRLC5W63GS6ZNIS2C7QYR7WF/graph.json","events_json":"https://pith.science/api/pith-number/EMKRLC5W63GS6ZNIS2C7QYR7WF/events.json","paper":"https://pith.science/paper/EMKRLC5W"},"agent_actions":{"view_html":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF","download_json":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF.json","view_paper":"https://pith.science/paper/EMKRLC5W","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.1855&json=true","fetch_graph":"https://pith.science/api/pith-number/EMKRLC5W63GS6ZNIS2C7QYR7WF/graph.json","fetch_events":"https://pith.science/api/pith-number/EMKRLC5W63GS6ZNIS2C7QYR7WF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF/action/storage_attestation","attest_author":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF/action/author_attestation","sign_citation":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF/action/citation_signature","submit_replication":"https://pith.science/pith/EMKRLC5W63GS6ZNIS2C7QYR7WF/action/replication_record"}},"created_at":"2026-05-18T03:51:26.730551+00:00","updated_at":"2026-05-18T03:51:26.730551+00:00"}