{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MPPG3ZRPUGE6VFRQRMVZ676WSN","short_pith_number":"pith:MPPG3ZRP","schema_version":"1.0","canonical_sha256":"63de6de62fa189ea96308b2b9f7fd693552dc9e3e8ba8f6400972db7d74e330a","source":{"kind":"arxiv","id":"1703.01405","version":1},"attestation_state":"computed","paper":{"title":"Convex recovery of continuous domain piecewise constant images from non-uniform Fourier samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Greg Ongie, Mathews Jacob, Sampurna Biswas","submitted_at":"2017-03-04T06:55:04Z","abstract_excerpt":"We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of a bandlimited function. This assumption induces linear dependencies between the Fourier coefficients of the image, which results in a two-fold block Toeplitz matrix constructed from the Fourier coefficients being low-rank. The proposed algorithm reformulates the recovery of the unknown Fourier coefficients as a structured low-rank matrix completion problem,"},"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":"1703.01405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-03-04T06:55:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"1fb240b56254e4809353f78998b044fab3e602d199044f8b40683d8389c6f503","abstract_canon_sha256":"2577395aa039cc97c8a0fef8264fcaadd6ddf07a25941b085c696ed47998d57b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:39.854853Z","signature_b64":"dkuZBsvm7i8/zaG6UOOWJAPJTs60Yn6aiq4MQNk9fYeJ1YJjtKHjXDQNkDRcDik6+IFI8n8MAiccUk7PX+f0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63de6de62fa189ea96308b2b9f7fd693552dc9e3e8ba8f6400972db7d74e330a","last_reissued_at":"2026-05-18T00:23:39.854227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:39.854227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex recovery of continuous domain piecewise constant images from non-uniform Fourier samples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Greg Ongie, Mathews Jacob, Sampurna Biswas","submitted_at":"2017-03-04T06:55:04Z","abstract_excerpt":"We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of a bandlimited function. This assumption induces linear dependencies between the Fourier coefficients of the image, which results in a two-fold block Toeplitz matrix constructed from the Fourier coefficients being low-rank. The proposed algorithm reformulates the recovery of the unknown Fourier coefficients as a structured low-rank matrix completion problem,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01405","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":"1703.01405","created_at":"2026-05-18T00:23:39.854339+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.01405v1","created_at":"2026-05-18T00:23:39.854339+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01405","created_at":"2026-05-18T00:23:39.854339+00:00"},{"alias_kind":"pith_short_12","alias_value":"MPPG3ZRPUGE6","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MPPG3ZRPUGE6VFRQ","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MPPG3ZRP","created_at":"2026-05-18T12:31:31.346846+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/MPPG3ZRPUGE6VFRQRMVZ676WSN","json":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN.json","graph_json":"https://pith.science/api/pith-number/MPPG3ZRPUGE6VFRQRMVZ676WSN/graph.json","events_json":"https://pith.science/api/pith-number/MPPG3ZRPUGE6VFRQRMVZ676WSN/events.json","paper":"https://pith.science/paper/MPPG3ZRP"},"agent_actions":{"view_html":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN","download_json":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN.json","view_paper":"https://pith.science/paper/MPPG3ZRP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.01405&json=true","fetch_graph":"https://pith.science/api/pith-number/MPPG3ZRPUGE6VFRQRMVZ676WSN/graph.json","fetch_events":"https://pith.science/api/pith-number/MPPG3ZRPUGE6VFRQRMVZ676WSN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN/action/storage_attestation","attest_author":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN/action/author_attestation","sign_citation":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN/action/citation_signature","submit_replication":"https://pith.science/pith/MPPG3ZRPUGE6VFRQRMVZ676WSN/action/replication_record"}},"created_at":"2026-05-18T00:23:39.854339+00:00","updated_at":"2026-05-18T00:23:39.854339+00:00"}