{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:FN5FH5AX7TJUALAILIX2PGTHLK","short_pith_number":"pith:FN5FH5AX","schema_version":"1.0","canonical_sha256":"2b7a53f417fcd3402c085a2fa79a675aa89188a42d48559a4a3ec0a66ff4b6b0","source":{"kind":"arxiv","id":"1103.1943","version":2},"attestation_state":"computed","paper":{"title":"Compressed Sensing over $\\ell_p$-balls: Minimax Mean Square Error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari, Arian Maleki, David Donoho, Iain Johnstone","submitted_at":"2011-03-10T06:04:40Z","abstract_excerpt":"We consider the compressed sensing problem, where the object $x_0 \\in \\bR^N$ is to be recovered from incomplete measurements $y = Ax_0 + z$; here the sensing matrix $A$ is an $n \\times N$ random matrix with iid Gaussian entries and $n < N$. A popular method of sparsity-promoting reconstruction is $\\ell^1$-penalized least-squares reconstruction (aka LASSO, Basis Pursuit).\n  It is currently popular to consider the strict sparsity model, where the object $x_0$ is nonzero in only a small fraction of entries. In this paper, we instead consider the much more broadly applicable $\\ell_p$-sparsity mode"},"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":"1103.1943","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-03-10T06:04:40Z","cross_cats_sorted":["math.IT","math.ST","stat.TH"],"title_canon_sha256":"3e54a1701789d73b1924d951b552e89482dc0b61e54968340cc184e82ba28505","abstract_canon_sha256":"dfabaaaef6e56c9a14ceef689b2b288fdd491938b4d2246e0b62d1d8d400015a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:01.286807Z","signature_b64":"aDQymAuIpc5bo6onJcwrMvrWu3saPRr7oV9ftfyqS8/qgVrKNvTk4TluTrp8u8RZ4Us4Lg7ygzkR8jez38AbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b7a53f417fcd3402c085a2fa79a675aa89188a42d48559a4a3ec0a66ff4b6b0","last_reissued_at":"2026-05-18T04:26:01.286374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:01.286374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compressed Sensing over $\\ell_p$-balls: Minimax Mean Square Error","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.ST","stat.TH"],"primary_cat":"cs.IT","authors_text":"Andrea Montanari, Arian Maleki, David Donoho, Iain Johnstone","submitted_at":"2011-03-10T06:04:40Z","abstract_excerpt":"We consider the compressed sensing problem, where the object $x_0 \\in \\bR^N$ is to be recovered from incomplete measurements $y = Ax_0 + z$; here the sensing matrix $A$ is an $n \\times N$ random matrix with iid Gaussian entries and $n < N$. A popular method of sparsity-promoting reconstruction is $\\ell^1$-penalized least-squares reconstruction (aka LASSO, Basis Pursuit).\n  It is currently popular to consider the strict sparsity model, where the object $x_0$ is nonzero in only a small fraction of entries. In this paper, we instead consider the much more broadly applicable $\\ell_p$-sparsity mode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1943","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":"1103.1943","created_at":"2026-05-18T04:26:01.286446+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1943v2","created_at":"2026-05-18T04:26:01.286446+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1943","created_at":"2026-05-18T04:26:01.286446+00:00"},{"alias_kind":"pith_short_12","alias_value":"FN5FH5AX7TJU","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_16","alias_value":"FN5FH5AX7TJUALAI","created_at":"2026-05-18T12:26:28.662955+00:00"},{"alias_kind":"pith_short_8","alias_value":"FN5FH5AX","created_at":"2026-05-18T12:26:28.662955+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/FN5FH5AX7TJUALAILIX2PGTHLK","json":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK.json","graph_json":"https://pith.science/api/pith-number/FN5FH5AX7TJUALAILIX2PGTHLK/graph.json","events_json":"https://pith.science/api/pith-number/FN5FH5AX7TJUALAILIX2PGTHLK/events.json","paper":"https://pith.science/paper/FN5FH5AX"},"agent_actions":{"view_html":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK","download_json":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK.json","view_paper":"https://pith.science/paper/FN5FH5AX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1943&json=true","fetch_graph":"https://pith.science/api/pith-number/FN5FH5AX7TJUALAILIX2PGTHLK/graph.json","fetch_events":"https://pith.science/api/pith-number/FN5FH5AX7TJUALAILIX2PGTHLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK/action/storage_attestation","attest_author":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK/action/author_attestation","sign_citation":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK/action/citation_signature","submit_replication":"https://pith.science/pith/FN5FH5AX7TJUALAILIX2PGTHLK/action/replication_record"}},"created_at":"2026-05-18T04:26:01.286446+00:00","updated_at":"2026-05-18T04:26:01.286446+00:00"}