{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:YZ3ZZKJLGIKZYDQDBL2S24U7GX","short_pith_number":"pith:YZ3ZZKJL","schema_version":"1.0","canonical_sha256":"c6779ca92b32159c0e030af52d729f35ce1e611c39be874cfd2a549e1e8f53a9","source":{"kind":"arxiv","id":"1510.02923","version":2},"attestation_state":"computed","paper":{"title":"On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.NA"],"primary_cat":"math.AP","authors_text":"Adrian Martin, Emanuele Schiavi, Sergio Segura de Leon","submitted_at":"2015-10-10T13:11:57Z","abstract_excerpt":"Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called $1$-Laplacian operator and special care is needed to properly formulate the problem. The rician statistics of the data are introduced through a singular equation with a reaction term defined in terms of modified first order Bessel functions. An existence theory is provided here together with other qualitative properties of the solutions. Remarkably, each po"},"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":"1510.02923","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-10T13:11:57Z","cross_cats_sorted":["cs.CV","math.NA"],"title_canon_sha256":"cc850b31ce35b478d7f628ee2246821d0d10aeef4ff3784c661277531aa6c9ae","abstract_canon_sha256":"e2fb7a7c7b4a0715332412945c69215f67348dd47f57e91a97f6c2dfed084b1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:58.380493Z","signature_b64":"7KORjJkX9fl8EXmmXpUYdvDNZ80g3dE2eB1UqyrQUAbXVcmmUEXHzQwqL2fQ4YN6YBTlKZS3VRkmCxrXI4TyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6779ca92b32159c0e030af52d729f35ce1e611c39be874cfd2a549e1e8f53a9","last_reissued_at":"2026-05-17T23:59:58.380040Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:58.380040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.NA"],"primary_cat":"math.AP","authors_text":"Adrian Martin, Emanuele Schiavi, Sergio Segura de Leon","submitted_at":"2015-10-10T13:11:57Z","abstract_excerpt":"Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called $1$-Laplacian operator and special care is needed to properly formulate the problem. The rician statistics of the data are introduced through a singular equation with a reaction term defined in terms of modified first order Bessel functions. An existence theory is provided here together with other qualitative properties of the solutions. Remarkably, each po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02923","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":"1510.02923","created_at":"2026-05-17T23:59:58.380108+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.02923v2","created_at":"2026-05-17T23:59:58.380108+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.02923","created_at":"2026-05-17T23:59:58.380108+00:00"},{"alias_kind":"pith_short_12","alias_value":"YZ3ZZKJLGIKZ","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_16","alias_value":"YZ3ZZKJLGIKZYDQD","created_at":"2026-05-18T12:29:52.810259+00:00"},{"alias_kind":"pith_short_8","alias_value":"YZ3ZZKJL","created_at":"2026-05-18T12:29:52.810259+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/YZ3ZZKJLGIKZYDQDBL2S24U7GX","json":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX.json","graph_json":"https://pith.science/api/pith-number/YZ3ZZKJLGIKZYDQDBL2S24U7GX/graph.json","events_json":"https://pith.science/api/pith-number/YZ3ZZKJLGIKZYDQDBL2S24U7GX/events.json","paper":"https://pith.science/paper/YZ3ZZKJL"},"agent_actions":{"view_html":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX","download_json":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX.json","view_paper":"https://pith.science/paper/YZ3ZZKJL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.02923&json=true","fetch_graph":"https://pith.science/api/pith-number/YZ3ZZKJLGIKZYDQDBL2S24U7GX/graph.json","fetch_events":"https://pith.science/api/pith-number/YZ3ZZKJLGIKZYDQDBL2S24U7GX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX/action/storage_attestation","attest_author":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX/action/author_attestation","sign_citation":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX/action/citation_signature","submit_replication":"https://pith.science/pith/YZ3ZZKJLGIKZYDQDBL2S24U7GX/action/replication_record"}},"created_at":"2026-05-17T23:59:58.380108+00:00","updated_at":"2026-05-17T23:59:58.380108+00:00"}