{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JHACQ5JGWY27QAZSCRL7YM4P3P","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":"4df4892585d122c817fcd6729f75df8b4cb60ddaa5ffd363549a1c7c152ae626","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-26T15:17:01Z","title_canon_sha256":"0d06515e6c874970c8623022f77063e002f133416c7b3c94bc656531b67d11a9"},"schema_version":"1.0","source":{"id":"0911.5098","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.5098","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"arxiv_version","alias_value":"0911.5098v1","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.5098","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"pith_short_12","alias_value":"JHACQ5JGWY27","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"pith_short_16","alias_value":"JHACQ5JGWY27QAZS","created_at":"2026-06-03T23:06:30Z"},{"alias_kind":"pith_short_8","alias_value":"JHACQ5JG","created_at":"2026-06-03T23:06:30Z"}],"graph_snapshots":[{"event_id":"sha256:53ca6ec0e22638cad9c7f5aff7beda74553826c79d6ab4cd8aacc66978f8605e","target":"graph","created_at":"2026-06-03T23:06:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0911.5098/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin to the projected Landweber algorithm is studied. This work extends recent progress made on the efficient inversion of finite dimensional linear systems under a sparsity constraint to the Hilbert space setting and to more general non-convex constraints.","authors_text":"Thomas Blumensath","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-26T15:17:01Z","title":"Non-convexly constrained linear inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5098","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":"sha256:01620b287aea9db03afa88f5af8ecb5818ae0936769fe961a53c3d319364b277","target":"record","created_at":"2026-06-03T23:06:30Z","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":"4df4892585d122c817fcd6729f75df8b4cb60ddaa5ffd363549a1c7c152ae626","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-11-26T15:17:01Z","title_canon_sha256":"0d06515e6c874970c8623022f77063e002f133416c7b3c94bc656531b67d11a9"},"schema_version":"1.0","source":{"id":"0911.5098","kind":"arxiv","version":1}},"canonical_sha256":"49c0287526b635f803321457fc338fdbc6fc4870d7afe1f1eea866b33ba812eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49c0287526b635f803321457fc338fdbc6fc4870d7afe1f1eea866b33ba812eb","first_computed_at":"2026-06-03T23:06:30.949575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:30.949575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MBUabocrzlHNrmEaIub2xeFd8rPAXJLMDGooRiNissLV3avMZuqkGEnEISPO9IgOsf6NrMDOPINOZwN5Dnz3Bw==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:30.949979Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.5098","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01620b287aea9db03afa88f5af8ecb5818ae0936769fe961a53c3d319364b277","sha256:53ca6ec0e22638cad9c7f5aff7beda74553826c79d6ab4cd8aacc66978f8605e"],"state_sha256":"47ff65e01a64860cbdb4db5dd6b8a5cde5bf8f427c233c102ec0fdfd3fccd2d0"}