{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5WY3HWOECKFSJO6KSBNO7JDWVD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"bf8077e3938438e76e3b0624e758b8dd50ede8f070ddfade590c7028fdaa5b33","cross_cats_sorted":["cs.CV","cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-11-20T03:22:45Z","title_canon_sha256":"41e5056c9f19ed6d85e5ff07989cba1ab003ceb06d994e5348aab437c4a4f04b"},"schema_version":"1.0","source":{"id":"1211.4657","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4657","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4657v2","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4657","created_at":"2026-05-18T02:52:49Z"},{"alias_kind":"pith_short_12","alias_value":"5WY3HWOECKFS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5WY3HWOECKFSJO6K","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5WY3HWOE","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:924e5db094f12a6cdb2f54e71f4b9576b3b4a5561a32d6db76f7dd5604b85ec1","target":"graph","created_at":"2026-05-18T02:52:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we investigate a new compressive sensing model for multi-channel sparse data where each channel can be represented as a hierarchical tree and different channels are highly correlated. Therefore, the full data could follow the forest structure and we call this property as \\emph{forest sparsity}. It exploits both intra- and inter- channel correlations and enriches the family of existing model-based compressive sensing theories. The proposed theory indicates that only $\\mathcal{O}(Tk+\\log(N/k))$ measurements are required for multi-channel data with forest sparsity, where $T$ is the","authors_text":"Chen Chen, Junzhou Huang, Yeqing Li","cross_cats":["cs.CV","cs.IT","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-11-20T03:22:45Z","title":"Forest Sparsity for Multi-channel Compressive Sensing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4657","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0cd7d07d20187e1ba63769911fe31b6726aeaece50a4e8be4a154e7b63064dcc","target":"record","created_at":"2026-05-18T02:52:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"bf8077e3938438e76e3b0624e758b8dd50ede8f070ddfade590c7028fdaa5b33","cross_cats_sorted":["cs.CV","cs.IT","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2012-11-20T03:22:45Z","title_canon_sha256":"41e5056c9f19ed6d85e5ff07989cba1ab003ceb06d994e5348aab437c4a4f04b"},"schema_version":"1.0","source":{"id":"1211.4657","kind":"arxiv","version":2}},"canonical_sha256":"edb1b3d9c4128b24bbca905aefa476a8cc9d569471ec6d18831e3078c3b586aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edb1b3d9c4128b24bbca905aefa476a8cc9d569471ec6d18831e3078c3b586aa","first_computed_at":"2026-05-18T02:52:49.664710Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:49.664710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sPAecTQxZ3KokS3/aCN/upKBEbjvRypNC29Kgizunm81mHNT6wpGu5I3Lu+6uYbl2XxUPWsNLsirYr6QzYmJAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:49.665080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4657","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cd7d07d20187e1ba63769911fe31b6726aeaece50a4e8be4a154e7b63064dcc","sha256:924e5db094f12a6cdb2f54e71f4b9576b3b4a5561a32d6db76f7dd5604b85ec1"],"state_sha256":"485952a06d3dd722cc2c48c42db38ae62c0d73a2a117f01e52de059743fde925"}