{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:2G4P4TLXQJ4XCQ5JRE3FV56EJE","short_pith_number":"pith:2G4P4TLX","schema_version":"1.0","canonical_sha256":"d1b8fe4d7782797143a989365af7c4492eae6be2e1011e3c3c3e4f27c42d928d","source":{"kind":"arxiv","id":"2208.10588","version":2},"attestation_state":"computed","paper":{"title":"Widely-Linear MMSE Estimation of Complex-Valued Graph Signals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"eess.SP","authors_text":"Alon Amar, Tirza Routtenberg","submitted_at":"2022-08-22T20:41:08Z","abstract_excerpt":"In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can achieve a lower mean-squared-error (MSE) than that of the linear minimum MSE (LMMSE) estimator. Inspired by the WLMMSE estimator, in this paper we develop the graph signal processing (GSP)-WLMMSE estimator, which minimizes the MSE among estimators that are represented as a two-channel output of a graph filter, i.e. widely-linear GSP estimators. We discuss the"},"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":"2208.10588","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SP","submitted_at":"2022-08-22T20:41:08Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"aa8d2bb61b9075315ec1224bbe8e0409a027358747280f2edcb3ce7ea6f2a2de","abstract_canon_sha256":"851f25f49a2afecf65148152450da8a0c633f3611e94671e3434dfccabdd43ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:26:16.266976Z","signature_b64":"7o4HTHek+3GcE+N+W15/LMRJeVwQR4FvTmxNtzyd5GbIJhMwpRc0VfiNjzIFQHl3jd+7HsMDir/fPTcgfqqIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1b8fe4d7782797143a989365af7c4492eae6be2e1011e3c3c3e4f27c42d928d","last_reissued_at":"2026-07-05T09:26:16.266556Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:26:16.266556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Widely-Linear MMSE Estimation of Complex-Valued Graph Signals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"eess.SP","authors_text":"Alon Amar, Tirza Routtenberg","submitted_at":"2022-08-22T20:41:08Z","abstract_excerpt":"In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can achieve a lower mean-squared-error (MSE) than that of the linear minimum MSE (LMMSE) estimator. Inspired by the WLMMSE estimator, in this paper we develop the graph signal processing (GSP)-WLMMSE estimator, which minimizes the MSE among estimators that are represented as a two-channel output of a graph filter, i.e. widely-linear GSP estimators. We discuss the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.10588","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.10588/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2208.10588","created_at":"2026-07-05T09:26:16.266622+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.10588v2","created_at":"2026-07-05T09:26:16.266622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.10588","created_at":"2026-07-05T09:26:16.266622+00:00"},{"alias_kind":"pith_short_12","alias_value":"2G4P4TLXQJ4X","created_at":"2026-07-05T09:26:16.266622+00:00"},{"alias_kind":"pith_short_16","alias_value":"2G4P4TLXQJ4XCQ5J","created_at":"2026-07-05T09:26:16.266622+00:00"},{"alias_kind":"pith_short_8","alias_value":"2G4P4TLX","created_at":"2026-07-05T09:26:16.266622+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/2G4P4TLXQJ4XCQ5JRE3FV56EJE","json":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE.json","graph_json":"https://pith.science/api/pith-number/2G4P4TLXQJ4XCQ5JRE3FV56EJE/graph.json","events_json":"https://pith.science/api/pith-number/2G4P4TLXQJ4XCQ5JRE3FV56EJE/events.json","paper":"https://pith.science/paper/2G4P4TLX"},"agent_actions":{"view_html":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE","download_json":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE.json","view_paper":"https://pith.science/paper/2G4P4TLX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.10588&json=true","fetch_graph":"https://pith.science/api/pith-number/2G4P4TLXQJ4XCQ5JRE3FV56EJE/graph.json","fetch_events":"https://pith.science/api/pith-number/2G4P4TLXQJ4XCQ5JRE3FV56EJE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE/action/storage_attestation","attest_author":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE/action/author_attestation","sign_citation":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE/action/citation_signature","submit_replication":"https://pith.science/pith/2G4P4TLXQJ4XCQ5JRE3FV56EJE/action/replication_record"}},"created_at":"2026-07-05T09:26:16.266622+00:00","updated_at":"2026-07-05T09:26:16.266622+00:00"}