{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:MUTBZBJE3C47M3QSSKH3PH7YCB","short_pith_number":"pith:MUTBZBJE","schema_version":"1.0","canonical_sha256":"65261c8524d8b9f66e12928fb79ff810676a6769df51d0cec307dd34e2a472d8","source":{"kind":"arxiv","id":"1607.08481","version":3},"attestation_state":"computed","paper":{"title":"A Nonlocal Denoising Algorithm for Manifold-Valued Images Using Second Order Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.CV","authors_text":"Friederike Laus, Gabriele Steidl, Johannes Persch, Mila Nikolova","submitted_at":"2016-07-28T14:39:13Z","abstract_excerpt":"Nonlocal patch-based methods, in particular the Bayes' approach of Lebrun, Buades and Morel (2013), are considered as state-of-the-art methods for denoising (color) images corrupted by white Gaussian noise of moderate variance. This paper is the first attempt to generalize this technique to manifold-valued images. Such images, for example images with phase or directional entries or with values in the manifold of symmetric positive definite matrices, are frequently encountered in real-world applications. Generalizing the normal law to manifolds is not canonical and different attempts have been "},"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":"1607.08481","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2016-07-28T14:39:13Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"580cdf508551f0c172e85315bb633923c2cf82987331e49c7d59a8c512454cd2","abstract_canon_sha256":"2a0e912b1e4be0b725f3086691b53fdba502a828c23a1eda73f42cd9db7d098e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:12.888357Z","signature_b64":"heFBrEjh5qWZlrtqBBYM1Dw8D0RAPOecFkdCxeofm9tAQGuT05XmTRg1aSUuPQx313U0rOIw+OasP1BWaBbIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65261c8524d8b9f66e12928fb79ff810676a6769df51d0cec307dd34e2a472d8","last_reissued_at":"2026-05-18T00:55:12.887865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:12.887865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Nonlocal Denoising Algorithm for Manifold-Valued Images Using Second Order Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"cs.CV","authors_text":"Friederike Laus, Gabriele Steidl, Johannes Persch, Mila Nikolova","submitted_at":"2016-07-28T14:39:13Z","abstract_excerpt":"Nonlocal patch-based methods, in particular the Bayes' approach of Lebrun, Buades and Morel (2013), are considered as state-of-the-art methods for denoising (color) images corrupted by white Gaussian noise of moderate variance. This paper is the first attempt to generalize this technique to manifold-valued images. Such images, for example images with phase or directional entries or with values in the manifold of symmetric positive definite matrices, are frequently encountered in real-world applications. Generalizing the normal law to manifolds is not canonical and different attempts have been "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08481","kind":"arxiv","version":3},"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":"1607.08481","created_at":"2026-05-18T00:55:12.887941+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.08481v3","created_at":"2026-05-18T00:55:12.887941+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.08481","created_at":"2026-05-18T00:55:12.887941+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUTBZBJE3C47","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUTBZBJE3C47M3QS","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUTBZBJE","created_at":"2026-05-18T12:30:32.724797+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/MUTBZBJE3C47M3QSSKH3PH7YCB","json":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB.json","graph_json":"https://pith.science/api/pith-number/MUTBZBJE3C47M3QSSKH3PH7YCB/graph.json","events_json":"https://pith.science/api/pith-number/MUTBZBJE3C47M3QSSKH3PH7YCB/events.json","paper":"https://pith.science/paper/MUTBZBJE"},"agent_actions":{"view_html":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB","download_json":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB.json","view_paper":"https://pith.science/paper/MUTBZBJE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.08481&json=true","fetch_graph":"https://pith.science/api/pith-number/MUTBZBJE3C47M3QSSKH3PH7YCB/graph.json","fetch_events":"https://pith.science/api/pith-number/MUTBZBJE3C47M3QSSKH3PH7YCB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB/action/storage_attestation","attest_author":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB/action/author_attestation","sign_citation":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB/action/citation_signature","submit_replication":"https://pith.science/pith/MUTBZBJE3C47M3QSSKH3PH7YCB/action/replication_record"}},"created_at":"2026-05-18T00:55:12.887941+00:00","updated_at":"2026-05-18T00:55:12.887941+00:00"}