{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:P2P2D5YKNOYT7XBOGEZNXVMUUN","short_pith_number":"pith:P2P2D5YK","schema_version":"1.0","canonical_sha256":"7e9fa1f70a6bb13fdc2e3132dbd594a354cb18ccdf6acf4d8972833790d99b1f","source":{"kind":"arxiv","id":"1708.06332","version":2},"attestation_state":"computed","paper":{"title":"Efficient Nonparametric Bayesian Inference For X-Ray Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Fran\\c{c}ois Monard, Gabriel P. Paternain, Richard Nickl","submitted_at":"2017-08-21T17:33:30Z","abstract_excerpt":"We consider the statistical inverse problem of recovering a function $f: M \\to \\mathbb R$, where $M$ is a smooth compact Riemannian manifold with boundary, from measurements of general $X$-ray transforms $I_a(f)$ of $f$, corrupted by additive Gaussian noise. For $M$ equal to the unit disk with `flat' geometry and $a=0$ this reduces to the standard Radon transform, but our general setting allows for anisotropic media $M$ and can further model local `attenuation' effects -- both highly relevant in practical imaging problems such as SPECT tomography. We propose a nonparametric Bayesian inference "},"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":"1708.06332","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-08-21T17:33:30Z","cross_cats_sorted":["math.AP","stat.ME","stat.TH"],"title_canon_sha256":"97f0d122c7a84695753ab5dcd5276740af15105728c708a9da2d57bb87153b97","abstract_canon_sha256":"dba4b57c5e6afaa0c865adfa59c4201ca60aa48087c92129f22a8da132193661"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:45.461830Z","signature_b64":"zCseBBG9tU2A0laOmB6pAiR69AFs6c9VYaYrlwQU/sMa8W06+o7+M1howmxtdSczx5BaYyG8cRLufPBBaz0CAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e9fa1f70a6bb13fdc2e3132dbd594a354cb18ccdf6acf4d8972833790d99b1f","last_reissued_at":"2026-05-18T00:23:45.461216Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:45.461216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Nonparametric Bayesian Inference For X-Ray Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Fran\\c{c}ois Monard, Gabriel P. Paternain, Richard Nickl","submitted_at":"2017-08-21T17:33:30Z","abstract_excerpt":"We consider the statistical inverse problem of recovering a function $f: M \\to \\mathbb R$, where $M$ is a smooth compact Riemannian manifold with boundary, from measurements of general $X$-ray transforms $I_a(f)$ of $f$, corrupted by additive Gaussian noise. For $M$ equal to the unit disk with `flat' geometry and $a=0$ this reduces to the standard Radon transform, but our general setting allows for anisotropic media $M$ and can further model local `attenuation' effects -- both highly relevant in practical imaging problems such as SPECT tomography. We propose a nonparametric Bayesian inference "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06332","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":"1708.06332","created_at":"2026-05-18T00:23:45.461306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.06332v2","created_at":"2026-05-18T00:23:45.461306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06332","created_at":"2026-05-18T00:23:45.461306+00:00"},{"alias_kind":"pith_short_12","alias_value":"P2P2D5YKNOYT","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"P2P2D5YKNOYT7XBO","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"P2P2D5YK","created_at":"2026-05-18T12:31:37.085036+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/P2P2D5YKNOYT7XBOGEZNXVMUUN","json":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN.json","graph_json":"https://pith.science/api/pith-number/P2P2D5YKNOYT7XBOGEZNXVMUUN/graph.json","events_json":"https://pith.science/api/pith-number/P2P2D5YKNOYT7XBOGEZNXVMUUN/events.json","paper":"https://pith.science/paper/P2P2D5YK"},"agent_actions":{"view_html":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN","download_json":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN.json","view_paper":"https://pith.science/paper/P2P2D5YK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.06332&json=true","fetch_graph":"https://pith.science/api/pith-number/P2P2D5YKNOYT7XBOGEZNXVMUUN/graph.json","fetch_events":"https://pith.science/api/pith-number/P2P2D5YKNOYT7XBOGEZNXVMUUN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN/action/storage_attestation","attest_author":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN/action/author_attestation","sign_citation":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN/action/citation_signature","submit_replication":"https://pith.science/pith/P2P2D5YKNOYT7XBOGEZNXVMUUN/action/replication_record"}},"created_at":"2026-05-18T00:23:45.461306+00:00","updated_at":"2026-05-18T00:23:45.461306+00:00"}