{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:CFZI7AMCQIHNKNVDWZDSB6HJKE","short_pith_number":"pith:CFZI7AMC","schema_version":"1.0","canonical_sha256":"11728f8182820ed536a3b64720f8e9513eaf127caa4e24fbaad411ef057add60","source":{"kind":"arxiv","id":"1406.1621","version":1},"attestation_state":"computed","paper":{"title":"Separable Cosparse Analysis Operator Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Julian W\\\"ormann, Martin Kleinsteuber, Matthias Seibert, R\\'emi Gribonval","submitted_at":"2014-06-06T09:33:59Z","abstract_excerpt":"The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose "},"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":"1406.1621","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-06-06T09:33:59Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"a4cb19e6f4d9e015477a4da903d0d730dee5faa4ac20a3256b711f0e325b39bc","abstract_canon_sha256":"ec51bef3aaf4b34f971103e48579ee25b8c55d6bffd1c103ee1c99bb7c96b457"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:22.035943Z","signature_b64":"X/XJhlguYEAX7xkgkMKMqHcLEyt5G6cgXqtbtEbcfdKjxbFkOzzLb7UVEEystufrQ+UQ5eCdmHh0tm1zwfyrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11728f8182820ed536a3b64720f8e9513eaf127caa4e24fbaad411ef057add60","last_reissued_at":"2026-05-18T02:50:22.035443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:22.035443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Separable Cosparse Analysis Operator Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Julian W\\\"ormann, Martin Kleinsteuber, Matthias Seibert, R\\'emi Gribonval","submitted_at":"2014-06-06T09:33:59Z","abstract_excerpt":"The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1621","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":"1406.1621","created_at":"2026-05-18T02:50:22.035501+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.1621v1","created_at":"2026-05-18T02:50:22.035501+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.1621","created_at":"2026-05-18T02:50:22.035501+00:00"},{"alias_kind":"pith_short_12","alias_value":"CFZI7AMCQIHN","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"CFZI7AMCQIHNKNVD","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"CFZI7AMC","created_at":"2026-05-18T12:28:22.404517+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/CFZI7AMCQIHNKNVDWZDSB6HJKE","json":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE.json","graph_json":"https://pith.science/api/pith-number/CFZI7AMCQIHNKNVDWZDSB6HJKE/graph.json","events_json":"https://pith.science/api/pith-number/CFZI7AMCQIHNKNVDWZDSB6HJKE/events.json","paper":"https://pith.science/paper/CFZI7AMC"},"agent_actions":{"view_html":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE","download_json":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE.json","view_paper":"https://pith.science/paper/CFZI7AMC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.1621&json=true","fetch_graph":"https://pith.science/api/pith-number/CFZI7AMCQIHNKNVDWZDSB6HJKE/graph.json","fetch_events":"https://pith.science/api/pith-number/CFZI7AMCQIHNKNVDWZDSB6HJKE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE/action/storage_attestation","attest_author":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE/action/author_attestation","sign_citation":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE/action/citation_signature","submit_replication":"https://pith.science/pith/CFZI7AMCQIHNKNVDWZDSB6HJKE/action/replication_record"}},"created_at":"2026-05-18T02:50:22.035501+00:00","updated_at":"2026-05-18T02:50:22.035501+00:00"}