{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CG2ZLPJGUSVA6VLOXIRYV5BDZD","short_pith_number":"pith:CG2ZLPJG","schema_version":"1.0","canonical_sha256":"11b595bd26a4aa0f556eba238af423c8e43925a14bc6cd90e02ed62e17bd3373","source":{"kind":"arxiv","id":"1109.0573","version":2},"attestation_state":"computed","paper":{"title":"Phase Retrieval via Matrix Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Emmanuel J. Candes, Thomas Strohmer, Vlad Voroninski, Yonina Eldar","submitted_at":"2011-09-02T22:52:18Z","abstract_excerpt":"This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent lite"},"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":"1109.0573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-09-02T22:52:18Z","cross_cats_sorted":["math.IT","math.NA"],"title_canon_sha256":"b7c18207e13b6234f06b2c1f1ac16c5bdfaf5042ba5aa68503e1d987d7f2d760","abstract_canon_sha256":"f5c3e99c1ccbe9aff8f3b626b33ec7c08f80c98592d8e65f93997a2348dcda5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:44.174552Z","signature_b64":"b8ZiduJTIehW1xfUlxp01WYxf2S7xNPIUry06JXXbiT8YIdLu4Rzwu9ijXpoaOgbDLaWEC4ubg6T1urw/LClAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11b595bd26a4aa0f556eba238af423c8e43925a14bc6cd90e02ed62e17bd3373","last_reissued_at":"2026-05-18T04:12:44.173823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:44.173823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase Retrieval via Matrix Completion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.NA"],"primary_cat":"cs.IT","authors_text":"Emmanuel J. Candes, Thomas Strohmer, Vlad Voroninski, Yonina Eldar","submitted_at":"2011-09-02T22:52:18Z","abstract_excerpt":"This paper develops a novel framework for phase retrieval, a problem which arises in X-ray crystallography, diffraction imaging, astronomical imaging and many other applications. Our approach combines multiple structured illuminations together with ideas from convex programming to recover the phase from intensity measurements, typically from the modulus of the diffracted wave. We demonstrate empirically that any complex-valued object can be recovered from the knowledge of the magnitude of just a few diffracted patterns by solving a simple convex optimization problem inspired by the recent lite"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0573","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":"1109.0573","created_at":"2026-05-18T04:12:44.173921+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.0573v2","created_at":"2026-05-18T04:12:44.173921+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0573","created_at":"2026-05-18T04:12:44.173921+00:00"},{"alias_kind":"pith_short_12","alias_value":"CG2ZLPJGUSVA","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CG2ZLPJGUSVA6VLO","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CG2ZLPJG","created_at":"2026-05-18T12:26:26.731475+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/CG2ZLPJGUSVA6VLOXIRYV5BDZD","json":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD.json","graph_json":"https://pith.science/api/pith-number/CG2ZLPJGUSVA6VLOXIRYV5BDZD/graph.json","events_json":"https://pith.science/api/pith-number/CG2ZLPJGUSVA6VLOXIRYV5BDZD/events.json","paper":"https://pith.science/paper/CG2ZLPJG"},"agent_actions":{"view_html":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD","download_json":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD.json","view_paper":"https://pith.science/paper/CG2ZLPJG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.0573&json=true","fetch_graph":"https://pith.science/api/pith-number/CG2ZLPJGUSVA6VLOXIRYV5BDZD/graph.json","fetch_events":"https://pith.science/api/pith-number/CG2ZLPJGUSVA6VLOXIRYV5BDZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD/action/storage_attestation","attest_author":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD/action/author_attestation","sign_citation":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD/action/citation_signature","submit_replication":"https://pith.science/pith/CG2ZLPJGUSVA6VLOXIRYV5BDZD/action/replication_record"}},"created_at":"2026-05-18T04:12:44.173921+00:00","updated_at":"2026-05-18T04:12:44.173921+00:00"}