{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WYYZ3PIBBNBEB2NM5DU2COLDIF","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":"6d44f11d71d07f19f27954c5af980e67cea73cdd37978b9640e759299fc3df5a","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-24T13:31:45Z","title_canon_sha256":"3e3b47194b67006e5f3458b38be81e71486b73a9926f74388b1475acf94ff32b"},"schema_version":"1.0","source":{"id":"1312.6813","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6813","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6813v3","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6813","created_at":"2026-05-18T02:52:14Z"},{"alias_kind":"pith_short_12","alias_value":"WYYZ3PIBBNBE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"WYYZ3PIBBNBEB2NM","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"WYYZ3PIB","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:f66321eaaeb4ef12d973ab27d4510a42a4223b139dbc31b539b84b140efb0fc3","target":"graph","created_at":"2026-05-18T02:52:14Z","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":"The least-square regression problems or inverse problems have been widely studied in many fields such as compressive sensing, signal processing, and image processing. To solve this kind of ill-posed problems, a regularization term (i.e., regularizer) should be introduced, under the assumption that the solutions have some specific properties, such as sparsity and group sparsity. Widely used regularizers include the $\\ell_1$ norm, total variation (TV) semi-norm, and so on.\n  Recently, a new regularization term with overlapping group sparsity has been considered. Majorization minimization iterati","authors_text":"Gang Liu, Jun Liu, Ting-Zhu Huang, Xiao-Guang Lv","cross_cats":["cs.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-24T13:31:45Z","title":"New explicit thresholding/shrinkage formulas for one class of regularization problems with overlapping group sparsity and their applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6813","kind":"arxiv","version":3},"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":"sha256:33c2e8af0f02787ba5fa52a3e4aab0d90d4b5b609a5212914d88bba9e04315a3","target":"record","created_at":"2026-05-18T02:52:14Z","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":"6d44f11d71d07f19f27954c5af980e67cea73cdd37978b9640e759299fc3df5a","cross_cats_sorted":["cs.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-12-24T13:31:45Z","title_canon_sha256":"3e3b47194b67006e5f3458b38be81e71486b73a9926f74388b1475acf94ff32b"},"schema_version":"1.0","source":{"id":"1312.6813","kind":"arxiv","version":3}},"canonical_sha256":"b6319dbd010b4240e9ace8e9a1396341632ea1c44fd81498606a28a8cd973f7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6319dbd010b4240e9ace8e9a1396341632ea1c44fd81498606a28a8cd973f7c","first_computed_at":"2026-05-18T02:52:14.112274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:14.112274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hn+tUyfN4W9PzvdqG2DIL/RhTf8HKR242LBp5Pre1Gnq9F+U2ty5FR4e6MWAVTqF2G7ZgdetrE8dfvfWf29BDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:14.112836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6813","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33c2e8af0f02787ba5fa52a3e4aab0d90d4b5b609a5212914d88bba9e04315a3","sha256:f66321eaaeb4ef12d973ab27d4510a42a4223b139dbc31b539b84b140efb0fc3"],"state_sha256":"e3535af3c2166bf76cec1e02212586b54a6aa7487eeeb7719601c0c0311babde"}