{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZS33UNMMJWODXISOFUFCT7P7FK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"258e56e9ca158d4176baf907e40e10cd1f7488692ed7d2fb5a60ab994746fd03","cross_cats_sorted":["cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T19:05:15Z","title_canon_sha256":"338c9397337199a807f27b346489e391f33199c94a4ea6a81d806d6697d27e68"},"schema_version":"1.0","source":{"id":"1907.08288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08288","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08288v1","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08288","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZS33UNMMJWOD","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"ZS33UNMMJWODXISO","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"ZS33UNMM","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:adf8b5dd45c1dcf104f06c950676777e168807eddd56de2b54421210100a4c46","target":"graph","created_at":"2026-05-17T23:40:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based tensor-tensor product and tensor SVD. We define a new transforms depended tensor rank and the corresponding tensor nuclear norm. Then we solve the TRPCA problem by convex optimization whose objective is a weighted combination of the new tensor nuclear norm and the $\\ell_1$-norm. In theory, we show that under certain incoherence conditions, the convex program exac","authors_text":"Canyi Lu, Pan Zhou","cross_cats":["cs.CV","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T19:05:15Z","title":"Exact Recovery of Tensor Robust Principal Component Analysis under Linear Transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08288","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d2e31137c31addeb81cd8a04fc339e29623b814e0e44cb32ffc3c7dcfda05ac5","target":"record","created_at":"2026-05-17T23:40:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"258e56e9ca158d4176baf907e40e10cd1f7488692ed7d2fb5a60ab994746fd03","cross_cats_sorted":["cs.CV","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-16T19:05:15Z","title_canon_sha256":"338c9397337199a807f27b346489e391f33199c94a4ea6a81d806d6697d27e68"},"schema_version":"1.0","source":{"id":"1907.08288","kind":"arxiv","version":1}},"canonical_sha256":"ccb7ba358c4d9c3ba24e2d0a29fdff2a8fa090a694baac9a080c982680e43bfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccb7ba358c4d9c3ba24e2d0a29fdff2a8fa090a694baac9a080c982680e43bfa","first_computed_at":"2026-05-17T23:40:10.327930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:10.327930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tPK35CszH2FYYiv0E9bDo0yf1Lf+L4smDJSu0F1d8vZ2Gh8jO2Ar04sYrjBhcqhfi6lUgZuLWve3AWZkJ7o9CQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:10.328410Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2e31137c31addeb81cd8a04fc339e29623b814e0e44cb32ffc3c7dcfda05ac5","sha256:adf8b5dd45c1dcf104f06c950676777e168807eddd56de2b54421210100a4c46"],"state_sha256":"bbd5f0790d48bd4b8250eed8e6f395f409c653e655fd20e10239ccbdb1a6fde8"}