{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ZFFFFLKTK73VQZVHBEAWTSIG3B","short_pith_number":"pith:ZFFFFLKT","schema_version":"1.0","canonical_sha256":"c94a52ad5357f75866a7090169c906d84e31fe4d23daca2186dfea2994e5ee90","source":{"kind":"arxiv","id":"1610.06098","version":2},"attestation_state":"computed","paper":{"title":"Leveraging Diversity and Sparsity in Blind Deconvolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ali Ahmed, Laurent Demanet","submitted_at":"2016-10-19T16:35:07Z","abstract_excerpt":"This paper considers recovering $L$-dimensional vectors $\\boldsymbol{w}$, and $\\boldsymbol{x}_1,\\boldsymbol{x}_2, \\ldots, \\boldsymbol{x}_N$ from their circular convolutions $\\boldsymbol{y}_n = \\boldsymbol{w}*\\boldsymbol{x}_n, \\ n = 1,2,3, \\ldots, N$. The vector $\\boldsymbol{w}$ is assumed to be $S$-sparse in a known basis that is spread out in the Fourier domain, and each input $\\boldsymbol{x}_n$ is a member of a known $K$-dimensional random subspace.\n  We prove that whenever $K + S\\log^2S \\lesssim L /\\log^4(LN)$, the problem can be solved effectively by using only the nuclear-norm minimizatio"},"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":"1610.06098","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-19T16:35:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"007ac3ca0bfa77b72966f1bc9f129ba275a826eccc07a97c9067dad28df76dcb","abstract_canon_sha256":"058d884d12276a4a82d6562fca81da9415db3f12ee1dd33cfa30d11180915d1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:57.604800Z","signature_b64":"Fjgfj9aNoLLhFfCOC2lZrjpW+cnE7MbQ6j7RrLdGpoMMljZ07PumnPNXLbdv+gDyQXQBwDhY1FmESviWP2x5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c94a52ad5357f75866a7090169c906d84e31fe4d23daca2186dfea2994e5ee90","last_reissued_at":"2026-05-18T00:27:57.604324Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:57.604324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Leveraging Diversity and Sparsity in Blind Deconvolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ali Ahmed, Laurent Demanet","submitted_at":"2016-10-19T16:35:07Z","abstract_excerpt":"This paper considers recovering $L$-dimensional vectors $\\boldsymbol{w}$, and $\\boldsymbol{x}_1,\\boldsymbol{x}_2, \\ldots, \\boldsymbol{x}_N$ from their circular convolutions $\\boldsymbol{y}_n = \\boldsymbol{w}*\\boldsymbol{x}_n, \\ n = 1,2,3, \\ldots, N$. The vector $\\boldsymbol{w}$ is assumed to be $S$-sparse in a known basis that is spread out in the Fourier domain, and each input $\\boldsymbol{x}_n$ is a member of a known $K$-dimensional random subspace.\n  We prove that whenever $K + S\\log^2S \\lesssim L /\\log^4(LN)$, the problem can be solved effectively by using only the nuclear-norm minimizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06098","kind":"arxiv","version":2},"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":"1610.06098","created_at":"2026-05-18T00:27:57.604392+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06098v2","created_at":"2026-05-18T00:27:57.604392+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06098","created_at":"2026-05-18T00:27:57.604392+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZFFFFLKTK73V","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZFFFFLKTK73VQZVH","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZFFFFLKT","created_at":"2026-05-18T12:30:53.716459+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/ZFFFFLKTK73VQZVHBEAWTSIG3B","json":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B.json","graph_json":"https://pith.science/api/pith-number/ZFFFFLKTK73VQZVHBEAWTSIG3B/graph.json","events_json":"https://pith.science/api/pith-number/ZFFFFLKTK73VQZVHBEAWTSIG3B/events.json","paper":"https://pith.science/paper/ZFFFFLKT"},"agent_actions":{"view_html":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B","download_json":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B.json","view_paper":"https://pith.science/paper/ZFFFFLKT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06098&json=true","fetch_graph":"https://pith.science/api/pith-number/ZFFFFLKTK73VQZVHBEAWTSIG3B/graph.json","fetch_events":"https://pith.science/api/pith-number/ZFFFFLKTK73VQZVHBEAWTSIG3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B/action/storage_attestation","attest_author":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B/action/author_attestation","sign_citation":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B/action/citation_signature","submit_replication":"https://pith.science/pith/ZFFFFLKTK73VQZVHBEAWTSIG3B/action/replication_record"}},"created_at":"2026-05-18T00:27:57.604392+00:00","updated_at":"2026-05-18T00:27:57.604392+00:00"}