{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:A3I2R7LLYMZAJXHGISZEROSGKF","short_pith_number":"pith:A3I2R7LL","schema_version":"1.0","canonical_sha256":"06d1a8fd6bc33204dce644b248ba46514a97fdd0f550d5f06ec3b87259ab0683","source":{"kind":"arxiv","id":"1504.01956","version":1},"attestation_state":"computed","paper":{"title":"Infimal convolution regularisation functionals of BV and $\\mathrm{L}^{p}$ spaces. Part I: The finite $p$ case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carola-Bibiane Sch\\\"onlieb, Evangelos Papoutsellis, Konstantinos Papafitsoros, Martin Burger","submitted_at":"2015-04-08T13:28:33Z","abstract_excerpt":"We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation ($\\mathrm{TV}$) seminorm and $\\mathrm{L}^{p}$ norms. A unified well-posedness analysis is presented and a detailed study of the one dimensional model is performed, by computing exact solutions for the corresponding denoising problem and the case $p=2$. Furthermore, the dependency of the regularisation properties of this infimal convolution approach to the choice of $p$ is studied. It turns out that in t"},"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":"1504.01956","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-04-08T13:28:33Z","cross_cats_sorted":[],"title_canon_sha256":"32104a076aa9029bca439e3d30a7660bc100ede7acb7fe9a0dbeb7402b8c3cd5","abstract_canon_sha256":"cc0c73c706f7e041ca23843d3b5b907caff2e9ecd603336d9f29fddb4a967be4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:17.689730Z","signature_b64":"YDXGG8+0fCIgYWPlLbE26nRNuLb8eySyVjantLP3u5zoEJj4jfUaodFMbVDkddKB0Zw0EJduDNw4VxPURhwgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06d1a8fd6bc33204dce644b248ba46514a97fdd0f550d5f06ec3b87259ab0683","last_reissued_at":"2026-05-18T02:19:17.689189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:17.689189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infimal convolution regularisation functionals of BV and $\\mathrm{L}^{p}$ spaces. Part I: The finite $p$ case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Carola-Bibiane Sch\\\"onlieb, Evangelos Papoutsellis, Konstantinos Papafitsoros, Martin Burger","submitted_at":"2015-04-08T13:28:33Z","abstract_excerpt":"We study a general class of infimal convolution type regularisation functionals suitable for applications in image processing. These functionals incorporate a combination of the total variation ($\\mathrm{TV}$) seminorm and $\\mathrm{L}^{p}$ norms. A unified well-posedness analysis is presented and a detailed study of the one dimensional model is performed, by computing exact solutions for the corresponding denoising problem and the case $p=2$. Furthermore, the dependency of the regularisation properties of this infimal convolution approach to the choice of $p$ is studied. It turns out that in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01956","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":"1504.01956","created_at":"2026-05-18T02:19:17.689268+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.01956v1","created_at":"2026-05-18T02:19:17.689268+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01956","created_at":"2026-05-18T02:19:17.689268+00:00"},{"alias_kind":"pith_short_12","alias_value":"A3I2R7LLYMZA","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"A3I2R7LLYMZAJXHG","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"A3I2R7LL","created_at":"2026-05-18T12:29:10.953037+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/A3I2R7LLYMZAJXHGISZEROSGKF","json":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF.json","graph_json":"https://pith.science/api/pith-number/A3I2R7LLYMZAJXHGISZEROSGKF/graph.json","events_json":"https://pith.science/api/pith-number/A3I2R7LLYMZAJXHGISZEROSGKF/events.json","paper":"https://pith.science/paper/A3I2R7LL"},"agent_actions":{"view_html":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF","download_json":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF.json","view_paper":"https://pith.science/paper/A3I2R7LL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.01956&json=true","fetch_graph":"https://pith.science/api/pith-number/A3I2R7LLYMZAJXHGISZEROSGKF/graph.json","fetch_events":"https://pith.science/api/pith-number/A3I2R7LLYMZAJXHGISZEROSGKF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF/action/storage_attestation","attest_author":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF/action/author_attestation","sign_citation":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF/action/citation_signature","submit_replication":"https://pith.science/pith/A3I2R7LLYMZAJXHGISZEROSGKF/action/replication_record"}},"created_at":"2026-05-18T02:19:17.689268+00:00","updated_at":"2026-05-18T02:19:17.689268+00:00"}