{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:G4OCRCYOA5ROKJVJDOUUPHRZ66","short_pith_number":"pith:G4OCRCYO","schema_version":"1.0","canonical_sha256":"371c288b0e0762e526a91ba9479e39f7878e265b09a3ab008c8b55e19399ab69","source":{"kind":"arxiv","id":"1407.7349","version":5},"attestation_state":"computed","paper":{"title":"Regularization and Numerical Solution of the Inverse Scattering Problem using Shearlet Frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.FA","authors_text":"Gitta Kutyniok, Philipp Petersen, Volker Mehrmann","submitted_at":"2014-07-28T08:05:24Z","abstract_excerpt":"Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of cartoon-like functions. Since functions in this class are asymptotically optimally sparsely approximated by shearlet frames, we consider shearlets as a means for regularization in a Tikhonov method. We analyze two approaches, namely solvers for the nonlinear problem and for the linearized problem obtained by the Born approximation technique. As example for the first cl"},"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":"1407.7349","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-28T08:05:24Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"bd1759d0f4964b7e686ecdf3c5e2c9f835443041482a9b419fe5a9c4f4603b2e","abstract_canon_sha256":"3c0181e9ec4b66547eec336120b7b76631f17fc4fa01fb6f7cbccbe4c748a026"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:38.976022Z","signature_b64":"lNjJNENDSD1ss+qjAKW3NG4zHZM06gm8LhJ30TdU0wWdJRozHGKvZ0e3H/Q7qnMbUYmRw0X1auLwyetLnMLlBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"371c288b0e0762e526a91ba9479e39f7878e265b09a3ab008c8b55e19399ab69","last_reissued_at":"2026-05-18T01:15:38.975199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:38.975199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Regularization and Numerical Solution of the Inverse Scattering Problem using Shearlet Frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.FA","authors_text":"Gitta Kutyniok, Philipp Petersen, Volker Mehrmann","submitted_at":"2014-07-28T08:05:24Z","abstract_excerpt":"Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of cartoon-like functions. Since functions in this class are asymptotically optimally sparsely approximated by shearlet frames, we consider shearlets as a means for regularization in a Tikhonov method. We analyze two approaches, namely solvers for the nonlinear problem and for the linearized problem obtained by the Born approximation technique. As example for the first cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7349","kind":"arxiv","version":5},"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":"1407.7349","created_at":"2026-05-18T01:15:38.975334+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.7349v5","created_at":"2026-05-18T01:15:38.975334+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7349","created_at":"2026-05-18T01:15:38.975334+00:00"},{"alias_kind":"pith_short_12","alias_value":"G4OCRCYOA5RO","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"G4OCRCYOA5ROKJVJ","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"G4OCRCYO","created_at":"2026-05-18T12:28:28.263976+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/G4OCRCYOA5ROKJVJDOUUPHRZ66","json":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66.json","graph_json":"https://pith.science/api/pith-number/G4OCRCYOA5ROKJVJDOUUPHRZ66/graph.json","events_json":"https://pith.science/api/pith-number/G4OCRCYOA5ROKJVJDOUUPHRZ66/events.json","paper":"https://pith.science/paper/G4OCRCYO"},"agent_actions":{"view_html":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66","download_json":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66.json","view_paper":"https://pith.science/paper/G4OCRCYO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.7349&json=true","fetch_graph":"https://pith.science/api/pith-number/G4OCRCYOA5ROKJVJDOUUPHRZ66/graph.json","fetch_events":"https://pith.science/api/pith-number/G4OCRCYOA5ROKJVJDOUUPHRZ66/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66/action/storage_attestation","attest_author":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66/action/author_attestation","sign_citation":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66/action/citation_signature","submit_replication":"https://pith.science/pith/G4OCRCYOA5ROKJVJDOUUPHRZ66/action/replication_record"}},"created_at":"2026-05-18T01:15:38.975334+00:00","updated_at":"2026-05-18T01:15:38.975334+00:00"}