{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:YUO5NFHF7GQLQ6GUYR6G4GDT5H","short_pith_number":"pith:YUO5NFHF","schema_version":"1.0","canonical_sha256":"c51dd694e5f9a0b878d4c47c6e1873e9ec303b56ec4efe37a3c3b921db7b020d","source":{"kind":"arxiv","id":"1612.03080","version":1},"attestation_state":"computed","paper":{"title":"Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Charles-Alban Deledalle (IMB), Joseph Salmon (LTCI), Nicolas Papadakis (IMB), Samuel Vaiter (IMB)","submitted_at":"2016-12-08T12:30:21Z","abstract_excerpt":"We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dim"},"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":"1612.03080","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2016-12-08T12:30:21Z","cross_cats_sorted":[],"title_canon_sha256":"fe08c26fa4f05f8cf4a09e3acb7a442382c033d2bf8694243764fb5daab8bb4c","abstract_canon_sha256":"3a939fe1970b68b07e48513dd7a4ca931a59b69f397335eace2df3fb03366db8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:26.526814Z","signature_b64":"8TQjpCNP8Q4ef5Ric4rsdQRCS2P0i+5Lt7URWYeZttVYwy1YtmauXlIc/LLCyfNaeJinruLjiAX6wX6m26AOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c51dd694e5f9a0b878d4c47c6e1873e9ec303b56ec4efe37a3c3b921db7b020d","last_reissued_at":"2026-05-18T00:55:26.526117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:26.526117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Characterizing the maximum parameter of the total-variation denoising through the pseudo-inverse of the divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Charles-Alban Deledalle (IMB), Joseph Salmon (LTCI), Nicolas Papadakis (IMB), Samuel Vaiter (IMB)","submitted_at":"2016-12-08T12:30:21Z","abstract_excerpt":"We focus on the maximum regularization parameter for anisotropic total-variation denoising. It corresponds to the minimum value of the regularization parameter above which the solution remains constant. While this value is well know for the Lasso, such a critical value has not been investigated in details for the total-variation. Though, it is of importance when tuning the regularization parameter as it allows fixing an upper-bound on the grid for which the optimal parameter is sought. We establish a closed form expression for the one-dimensional case, as well as an upper-bound for the two-dim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03080","kind":"arxiv","version":1},"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":"1612.03080","created_at":"2026-05-18T00:55:26.526219+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.03080v1","created_at":"2026-05-18T00:55:26.526219+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03080","created_at":"2026-05-18T00:55:26.526219+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUO5NFHF7GQL","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUO5NFHF7GQLQ6GU","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUO5NFHF","created_at":"2026-05-18T12:30:53.716459+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/YUO5NFHF7GQLQ6GUYR6G4GDT5H","json":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H.json","graph_json":"https://pith.science/api/pith-number/YUO5NFHF7GQLQ6GUYR6G4GDT5H/graph.json","events_json":"https://pith.science/api/pith-number/YUO5NFHF7GQLQ6GUYR6G4GDT5H/events.json","paper":"https://pith.science/paper/YUO5NFHF"},"agent_actions":{"view_html":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H","download_json":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H.json","view_paper":"https://pith.science/paper/YUO5NFHF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.03080&json=true","fetch_graph":"https://pith.science/api/pith-number/YUO5NFHF7GQLQ6GUYR6G4GDT5H/graph.json","fetch_events":"https://pith.science/api/pith-number/YUO5NFHF7GQLQ6GUYR6G4GDT5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H/action/storage_attestation","attest_author":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H/action/author_attestation","sign_citation":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H/action/citation_signature","submit_replication":"https://pith.science/pith/YUO5NFHF7GQLQ6GUYR6G4GDT5H/action/replication_record"}},"created_at":"2026-05-18T00:55:26.526219+00:00","updated_at":"2026-05-18T00:55:26.526219+00:00"}