{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GU5L43PAROS47LTYSN44LYWLEZ","short_pith_number":"pith:GU5L43PA","schema_version":"1.0","canonical_sha256":"353abe6de08ba5cfae789379c5e2cb265a8639a23bcbbfb9c11470a93bb04309","source":{"kind":"arxiv","id":"1704.00835","version":5},"attestation_state":"computed","paper":{"title":"Near-Optimality of Linear Recovery from Indirect Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anatoli Juditsky, Arkadi Nemirovski","submitted_at":"2017-04-03T23:55:18Z","abstract_excerpt":"We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set ${\\cal X}$ from indirect observation $\\omega=Ax+\\xi$ of $x$ corrupted by random noise $\\xi$ with finite covariance matrix. It is shown that under some assumptions on ${\\cal X}$ (satisfied, e.g., when ${\\cal X}$ is the intersection of $K$ concentric ellipsoids/elliptic cylinders, or the unit ball of the spectral norm in the space of matrices) and on the norm $\\|\\cdot\\|$ used to measure the recovery error (satisfied, e.g., by $\\|\\cdot\\|_p$-norms, $1\\leq p\\leq 2$, on ${\\mathbf{R}}"},"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":"1704.00835","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-04-03T23:55:18Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"8f47235905bde8b7061ae8f26cfae904ff3ca72f8bf233c4403c3ddeb0660613","abstract_canon_sha256":"8121aa9a94e0632ee685aef3b54e85f3c71325359d9bf3f7576c57e8cda58590"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:06.288812Z","signature_b64":"Bb4NxqqTujN8nC3f4ZSe9fdw8c19aDQoThjAhlySQa4WJaeawiWkgjO//SQYvTmUYnscqYCn14OWo5XMWjn1DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"353abe6de08ba5cfae789379c5e2cb265a8639a23bcbbfb9c11470a93bb04309","last_reissued_at":"2026-05-17T23:51:06.288381Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:06.288381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Near-Optimality of Linear Recovery from Indirect Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Anatoli Juditsky, Arkadi Nemirovski","submitted_at":"2017-04-03T23:55:18Z","abstract_excerpt":"We consider the problem of recovering linear image $Bx$ of a signal $x$ known to belong to a given convex compact set ${\\cal X}$ from indirect observation $\\omega=Ax+\\xi$ of $x$ corrupted by random noise $\\xi$ with finite covariance matrix. It is shown that under some assumptions on ${\\cal X}$ (satisfied, e.g., when ${\\cal X}$ is the intersection of $K$ concentric ellipsoids/elliptic cylinders, or the unit ball of the spectral norm in the space of matrices) and on the norm $\\|\\cdot\\|$ used to measure the recovery error (satisfied, e.g., by $\\|\\cdot\\|_p$-norms, $1\\leq p\\leq 2$, on ${\\mathbf{R}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.00835","kind":"arxiv","version":5},"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":"1704.00835","created_at":"2026-05-17T23:51:06.288445+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.00835v5","created_at":"2026-05-17T23:51:06.288445+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.00835","created_at":"2026-05-17T23:51:06.288445+00:00"},{"alias_kind":"pith_short_12","alias_value":"GU5L43PAROS4","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GU5L43PAROS47LTY","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GU5L43PA","created_at":"2026-05-18T12:31:18.294218+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/GU5L43PAROS47LTYSN44LYWLEZ","json":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ.json","graph_json":"https://pith.science/api/pith-number/GU5L43PAROS47LTYSN44LYWLEZ/graph.json","events_json":"https://pith.science/api/pith-number/GU5L43PAROS47LTYSN44LYWLEZ/events.json","paper":"https://pith.science/paper/GU5L43PA"},"agent_actions":{"view_html":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ","download_json":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ.json","view_paper":"https://pith.science/paper/GU5L43PA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.00835&json=true","fetch_graph":"https://pith.science/api/pith-number/GU5L43PAROS47LTYSN44LYWLEZ/graph.json","fetch_events":"https://pith.science/api/pith-number/GU5L43PAROS47LTYSN44LYWLEZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ/action/storage_attestation","attest_author":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ/action/author_attestation","sign_citation":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ/action/citation_signature","submit_replication":"https://pith.science/pith/GU5L43PAROS47LTYSN44LYWLEZ/action/replication_record"}},"created_at":"2026-05-17T23:51:06.288445+00:00","updated_at":"2026-05-17T23:51:06.288445+00:00"}