{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J2WNTFNMB3QI6LKKGUDQAB2SD7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1f5e5cff7df29a84eb05ffc975356d047f4dda3ac9b5a98130f0424674fbf26b","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-04T00:57:43Z","title_canon_sha256":"5265a8f008f6af9e3d0fd4e8ca1232dd95cee04434f5654b48d987d220a28bca"},"schema_version":"1.0","source":{"id":"1310.1141","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1141","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1141v1","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1141","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"J2WNTFNMB3QI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J2WNTFNMB3QI6LKK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J2WNTFNM","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:32d839097e7a52dc5b30870909711a80e76317b69b319bee6e4b03cd7797e1cc","target":"graph","created_at":"2026-05-18T03:11:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The purpose of this paper is to report on recent approaches to reconstruction problems based on analog, or in other words, infinite-dimensional, image and signal models. We describe three main contributions to this problem. First, linear reconstructions from sampled measurements via so-called generalized sampling (GS). Second, the extension of generalized sampling to inverse and ill-posed problems. And third, the combination of generalized sampling with sparse recovery techniques. This final contribution leads to a theory and set of methods for infinite-dimensional compressed sensing, or as we","authors_text":"Anders Hansen, Ben Adcock, Bogdan Roman, Gerd Teschke","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-04T00:57:43Z","title":"Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1141","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f85b4cab678bbd6e9691343c3afa6087297b820a6ea33efb348d9d8cf5f1fd16","target":"record","created_at":"2026-05-18T03:11:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1f5e5cff7df29a84eb05ffc975356d047f4dda3ac9b5a98130f0424674fbf26b","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-10-04T00:57:43Z","title_canon_sha256":"5265a8f008f6af9e3d0fd4e8ca1232dd95cee04434f5654b48d987d220a28bca"},"schema_version":"1.0","source":{"id":"1310.1141","kind":"arxiv","version":1}},"canonical_sha256":"4eacd995ac0ee08f2d4a35070007521fc4de2e11dc5d2dd9d9cd5f02a034ace6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4eacd995ac0ee08f2d4a35070007521fc4de2e11dc5d2dd9d9cd5f02a034ace6","first_computed_at":"2026-05-18T03:11:23.422210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:23.422210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gdopWmjkbaQkKrstk+f/G5Co+t1Ins3J3op+hb7Eb6Pd2Bl3sAJ9JxWwA8UTu9HM8trhVIFeEBSrnXzLiviLCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:23.422962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1141","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f85b4cab678bbd6e9691343c3afa6087297b820a6ea33efb348d9d8cf5f1fd16","sha256:32d839097e7a52dc5b30870909711a80e76317b69b319bee6e4b03cd7797e1cc"],"state_sha256":"50eb1d62c87fd536205c68af960bb3f0d4b951ce5f32849d63e5afdc773eb20d"}