{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:E5PMVUTW2SMMPUPYANXIJYWY2I","short_pith_number":"pith:E5PMVUTW","schema_version":"1.0","canonical_sha256":"275ecad276d498c7d1f8036e84e2d8d2378308d4bba80b2362b82875fa152342","source":{"kind":"arxiv","id":"1204.3212","version":2},"attestation_state":"computed","paper":{"title":"Local Behavior of Sparse Analysis Regularization: Applications to Risk Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Charles Deledalle (CEREMADE), Charles Dossal (IMB), Gabriel Peyr\\'e (CEREMADE), Jalal Fadili (GREYC), Samuel Vaiter (CEREMADE)","submitted_at":"2012-04-14T20:30:55Z","abstract_excerpt":"In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we impose an analysis sparsity prior. More precisely, the recovery is cast as a convex optimization program where the objective is the sum of a quadratic data fidelity term and a regularization term formed of the L1-norm of the correlations between the sought after signal and atoms in a given (generally overcomplete) dictionary. The L1-sparsity analysis prior is "},"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":"1204.3212","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2012-04-14T20:30:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"6748eb2c0262c2f67de58227687ae399c2683d28868a7029cce1c20fe784b587","abstract_canon_sha256":"84c6c0c957c068dd57e4cd27db692e04ea8de12813036e1fdd05a2632be90cf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:14.658128Z","signature_b64":"M0PTiaaa3Y6Q/bEjeVdgKUKUF/Kq1BjlMcPV6s+Jnqz9SD98tjRY9GrtMFeQYnHXIBPV/Erdmoe6KzYMg3c3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"275ecad276d498c7d1f8036e84e2d8d2378308d4bba80b2362b82875fa152342","last_reissued_at":"2026-05-18T03:08:14.657519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:14.657519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Behavior of Sparse Analysis Regularization: Applications to Risk Estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Charles Deledalle (CEREMADE), Charles Dossal (IMB), Gabriel Peyr\\'e (CEREMADE), Jalal Fadili (GREYC), Samuel Vaiter (CEREMADE)","submitted_at":"2012-04-14T20:30:55Z","abstract_excerpt":"In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we impose an analysis sparsity prior. More precisely, the recovery is cast as a convex optimization program where the objective is the sum of a quadratic data fidelity term and a regularization term formed of the L1-norm of the correlations between the sought after signal and atoms in a given (generally overcomplete) dictionary. The L1-sparsity analysis prior is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3212","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":"1204.3212","created_at":"2026-05-18T03:08:14.657608+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.3212v2","created_at":"2026-05-18T03:08:14.657608+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3212","created_at":"2026-05-18T03:08:14.657608+00:00"},{"alias_kind":"pith_short_12","alias_value":"E5PMVUTW2SMM","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_16","alias_value":"E5PMVUTW2SMMPUPY","created_at":"2026-05-18T12:27:04.183437+00:00"},{"alias_kind":"pith_short_8","alias_value":"E5PMVUTW","created_at":"2026-05-18T12:27:04.183437+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/E5PMVUTW2SMMPUPYANXIJYWY2I","json":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I.json","graph_json":"https://pith.science/api/pith-number/E5PMVUTW2SMMPUPYANXIJYWY2I/graph.json","events_json":"https://pith.science/api/pith-number/E5PMVUTW2SMMPUPYANXIJYWY2I/events.json","paper":"https://pith.science/paper/E5PMVUTW"},"agent_actions":{"view_html":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I","download_json":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I.json","view_paper":"https://pith.science/paper/E5PMVUTW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.3212&json=true","fetch_graph":"https://pith.science/api/pith-number/E5PMVUTW2SMMPUPYANXIJYWY2I/graph.json","fetch_events":"https://pith.science/api/pith-number/E5PMVUTW2SMMPUPYANXIJYWY2I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I/action/storage_attestation","attest_author":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I/action/author_attestation","sign_citation":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I/action/citation_signature","submit_replication":"https://pith.science/pith/E5PMVUTW2SMMPUPYANXIJYWY2I/action/replication_record"}},"created_at":"2026-05-18T03:08:14.657608+00:00","updated_at":"2026-05-18T03:08:14.657608+00:00"}