{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HHNYAE4LNXDU3VIJS7KBUOTYWN","short_pith_number":"pith:HHNYAE4L","schema_version":"1.0","canonical_sha256":"39db80138b6dc74dd50997d41a3a78b34a6e1d92e3b3195e55b52958a30215e1","source":{"kind":"arxiv","id":"1705.09992","version":3},"attestation_state":"computed","paper":{"title":"LAP: a Linearize and Project Method for Solving Inverse Problems with Coupled Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"James Herring, James Nagy, Lars Ruthotto","submitted_at":"2017-05-28T21:11:53Z","abstract_excerpt":"Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image super-resolution requires joint estimation of the image and motion parameters from noisy measurements. Exploiting this structure is key for efficiently solving these large-scale optimization problems, which are often ill-conditioned.\n  In this paper, we present a new method called Linearize And Project (LAP) that offers a flexible framework for solving inverse problems with coupled variables. LAP is most promising for cases when th"},"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":"1705.09992","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-05-28T21:11:53Z","cross_cats_sorted":["cs.CV","cs.NA","math.OC"],"title_canon_sha256":"e527e84bc19d96865cbd8d20c36ee04b74f4049d194a477dd023af97275d4798","abstract_canon_sha256":"008f6bdc77a2bf40a392a8b610f8a4afc6fbbde6aedca41a6337dc64f74d1479"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:31.118270Z","signature_b64":"84FTmpXbhb0CuSZfTCEmtybJt9mL7/c3q5r7jMVDi//j81m3PyhtdpnXUN2SGhPpYmL6z/Ibxvske4cFHRtNAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39db80138b6dc74dd50997d41a3a78b34a6e1d92e3b3195e55b52958a30215e1","last_reissued_at":"2026-05-17T23:42:31.117418Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:31.117418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"LAP: a Linearize and Project Method for Solving Inverse Problems with Coupled Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"James Herring, James Nagy, Lars Ruthotto","submitted_at":"2017-05-28T21:11:53Z","abstract_excerpt":"Many inverse problems involve two or more sets of variables that represent different physical quantities but are tightly coupled with each other. For example, image super-resolution requires joint estimation of the image and motion parameters from noisy measurements. Exploiting this structure is key for efficiently solving these large-scale optimization problems, which are often ill-conditioned.\n  In this paper, we present a new method called Linearize And Project (LAP) that offers a flexible framework for solving inverse problems with coupled variables. LAP is most promising for cases when th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09992","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":"1705.09992","created_at":"2026-05-17T23:42:31.117561+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.09992v3","created_at":"2026-05-17T23:42:31.117561+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09992","created_at":"2026-05-17T23:42:31.117561+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHNYAE4LNXDU","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHNYAE4LNXDU3VIJ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHNYAE4L","created_at":"2026-05-18T12:31:18.294218+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/HHNYAE4LNXDU3VIJS7KBUOTYWN","json":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN.json","graph_json":"https://pith.science/api/pith-number/HHNYAE4LNXDU3VIJS7KBUOTYWN/graph.json","events_json":"https://pith.science/api/pith-number/HHNYAE4LNXDU3VIJS7KBUOTYWN/events.json","paper":"https://pith.science/paper/HHNYAE4L"},"agent_actions":{"view_html":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN","download_json":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN.json","view_paper":"https://pith.science/paper/HHNYAE4L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.09992&json=true","fetch_graph":"https://pith.science/api/pith-number/HHNYAE4LNXDU3VIJS7KBUOTYWN/graph.json","fetch_events":"https://pith.science/api/pith-number/HHNYAE4LNXDU3VIJS7KBUOTYWN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN/action/storage_attestation","attest_author":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN/action/author_attestation","sign_citation":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN/action/citation_signature","submit_replication":"https://pith.science/pith/HHNYAE4LNXDU3VIJS7KBUOTYWN/action/replication_record"}},"created_at":"2026-05-17T23:42:31.117561+00:00","updated_at":"2026-05-17T23:42:31.117561+00:00"}