{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:TO6X5PMRIASUXQFHWS22PECH7R","short_pith_number":"pith:TO6X5PMR","schema_version":"1.0","canonical_sha256":"9bbd7ebd9140254bc0a7b4b5a79047fc5f3a3db7875a9fa1d44dec617ae9805b","source":{"kind":"arxiv","id":"1503.05293","version":1},"attestation_state":"computed","paper":{"title":"Spectral Representations of One-Homogeneous Functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NA","authors_text":"Guy Gilboa, Lina Eckardt, Martin Burger, Michael Moeller","submitted_at":"2015-03-18T07:15:04Z","abstract_excerpt":"This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or $\\ell^1$-norms. Those functionals serve as a substitute for a Hilbert space structure (and the related norm) in classical linear spectral transforms, e.g. Fourier and wavelet analysis. We discuss three meaningful definitions of spectral representations by scale space and variational methods and prove that (nonlinear) eigenfunctions of the regularization functionals are indeed atoms in the spectral representation. Moreover, we verify further use"},"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":"1503.05293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-03-18T07:15:04Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4b2cebb9c878fe900473b9ac3dc21fc9f0d7e82bf91f70d482fa6e49cacf5800","abstract_canon_sha256":"9e5ca50ce1238b7971df83efa644ef6a12225d097d8af1135991d8ce34ec4a7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:50.856731Z","signature_b64":"kzBaaOEUy/otMQpb6Ggfca36FL8rL3ueAjiaZNP4Kroq3ntWylGsc8rTqrzqFCCXS7vGFxkLSmkJ4T1GRsjOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bbd7ebd9140254bc0a7b4b5a79047fc5f3a3db7875a9fa1d44dec617ae9805b","last_reissued_at":"2026-05-18T02:21:50.856115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:50.856115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral Representations of One-Homogeneous Functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NA","authors_text":"Guy Gilboa, Lina Eckardt, Martin Burger, Michael Moeller","submitted_at":"2015-03-18T07:15:04Z","abstract_excerpt":"This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or $\\ell^1$-norms. Those functionals serve as a substitute for a Hilbert space structure (and the related norm) in classical linear spectral transforms, e.g. Fourier and wavelet analysis. We discuss three meaningful definitions of spectral representations by scale space and variational methods and prove that (nonlinear) eigenfunctions of the regularization functionals are indeed atoms in the spectral representation. Moreover, we verify further use"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05293","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":"1503.05293","created_at":"2026-05-18T02:21:50.856200+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.05293v1","created_at":"2026-05-18T02:21:50.856200+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05293","created_at":"2026-05-18T02:21:50.856200+00:00"},{"alias_kind":"pith_short_12","alias_value":"TO6X5PMRIASU","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_16","alias_value":"TO6X5PMRIASUXQFH","created_at":"2026-05-18T12:29:42.218222+00:00"},{"alias_kind":"pith_short_8","alias_value":"TO6X5PMR","created_at":"2026-05-18T12:29:42.218222+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/TO6X5PMRIASUXQFHWS22PECH7R","json":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R.json","graph_json":"https://pith.science/api/pith-number/TO6X5PMRIASUXQFHWS22PECH7R/graph.json","events_json":"https://pith.science/api/pith-number/TO6X5PMRIASUXQFHWS22PECH7R/events.json","paper":"https://pith.science/paper/TO6X5PMR"},"agent_actions":{"view_html":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R","download_json":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R.json","view_paper":"https://pith.science/paper/TO6X5PMR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.05293&json=true","fetch_graph":"https://pith.science/api/pith-number/TO6X5PMRIASUXQFHWS22PECH7R/graph.json","fetch_events":"https://pith.science/api/pith-number/TO6X5PMRIASUXQFHWS22PECH7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R/action/storage_attestation","attest_author":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R/action/author_attestation","sign_citation":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R/action/citation_signature","submit_replication":"https://pith.science/pith/TO6X5PMRIASUXQFHWS22PECH7R/action/replication_record"}},"created_at":"2026-05-18T02:21:50.856200+00:00","updated_at":"2026-05-18T02:21:50.856200+00:00"}