{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:6J5HMPDEGPGFGHOVA4EGT6IRDZ","short_pith_number":"pith:6J5HMPDE","canonical_record":{"source":{"id":"2005.00959","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-05-03T00:58:23Z","cross_cats_sorted":["cs.CV","cs.LG","cs.NA","math.NA","stat.ML"],"title_canon_sha256":"628f71eaabebcd7ace7fa98085f2ff724223e96c7e86469c02b8922dd09db949","abstract_canon_sha256":"41bcd4d30202d27c4551b6053a8df457472d47429ba5c799dd431107b980c355"},"schema_version":"1.0"},"canonical_sha256":"f27a763c6433cc531dd5070869f9111e7eecce262a4a793750c13ee394e6b397","source":{"kind":"arxiv","id":"2005.00959","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.00959","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"2005.00959v3","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.00959","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"6J5HMPDEGPGF","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"pith_short_16","alias_value":"6J5HMPDEGPGFGHOV","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"pith_short_8","alias_value":"6J5HMPDE","created_at":"2026-07-05T03:04:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:6J5HMPDEGPGFGHOVA4EGT6IRDZ","target":"record","payload":{"canonical_record":{"source":{"id":"2005.00959","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-05-03T00:58:23Z","cross_cats_sorted":["cs.CV","cs.LG","cs.NA","math.NA","stat.ML"],"title_canon_sha256":"628f71eaabebcd7ace7fa98085f2ff724223e96c7e86469c02b8922dd09db949","abstract_canon_sha256":"41bcd4d30202d27c4551b6053a8df457472d47429ba5c799dd431107b980c355"},"schema_version":"1.0"},"canonical_sha256":"f27a763c6433cc531dd5070869f9111e7eecce262a4a793750c13ee394e6b397","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:04:01.043356Z","signature_b64":"YLoqaS4Rl/3GpoSg0zh+dzL2nJZ/VXtOEuD/1dNxiu0mKQFR0hmvI1Zg8jbRpigxav8TNuUQhpgznzdwjoIGAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f27a763c6433cc531dd5070869f9111e7eecce262a4a793750c13ee394e6b397","last_reissued_at":"2026-07-05T03:04:01.042858Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:04:01.042858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2005.00959","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zr57Jal6JTfdbwxUr+qnxFFwBl5dg/KZjisGcvHVf2byqKezFGP7bn2EwM6mdiq6S1DRf1nZ0617HxLpaBKbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T17:20:37.756058Z"},"content_sha256":"5a12c0281a401e77af34385f70ffb02b01569ec548dc42715a86b943532eb94c","schema_version":"1.0","event_id":"sha256:5a12c0281a401e77af34385f70ffb02b01569ec548dc42715a86b943532eb94c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:6J5HMPDEGPGFGHOVA4EGT6IRDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Convergence Rate of Projected Gradient Descent for a Back-Projection based Objective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.LG","cs.NA","math.NA","stat.ML"],"primary_cat":"math.OC","authors_text":"Raja Giryes, Tom Tirer","submitted_at":"2020-05-03T00:58:23Z","abstract_excerpt":"Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection (BP) based fidelity term as an alternative to the common least squares (LS), and demonstrated excellent results for popular inverse problems. These works have also empirically shown that using the BP term, rather than the LS term, requires fewer iterations of optimization algorithms. In this paper, we examine the convergence rate of the projected gradient d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.00959","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.00959/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:04:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g96hjOd3ifxEAqvDEuF3jMcAgISyIZROt5lg+uLluXQpYh7DeE3Xnx8L98sE2L+XL+ASmux13SJEhan3BuSrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T17:20:37.756641Z"},"content_sha256":"83315cc59ef3778fc9e3a29109ae17afe3063f718e23c9890f990b212c4102d4","schema_version":"1.0","event_id":"sha256:83315cc59ef3778fc9e3a29109ae17afe3063f718e23c9890f990b212c4102d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6J5HMPDEGPGFGHOVA4EGT6IRDZ/bundle.json","state_url":"https://pith.science/pith/6J5HMPDEGPGFGHOVA4EGT6IRDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6J5HMPDEGPGFGHOVA4EGT6IRDZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-06T17:20:37Z","links":{"resolver":"https://pith.science/pith/6J5HMPDEGPGFGHOVA4EGT6IRDZ","bundle":"https://pith.science/pith/6J5HMPDEGPGFGHOVA4EGT6IRDZ/bundle.json","state":"https://pith.science/pith/6J5HMPDEGPGFGHOVA4EGT6IRDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6J5HMPDEGPGFGHOVA4EGT6IRDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:6J5HMPDEGPGFGHOVA4EGT6IRDZ","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":"41bcd4d30202d27c4551b6053a8df457472d47429ba5c799dd431107b980c355","cross_cats_sorted":["cs.CV","cs.LG","cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-05-03T00:58:23Z","title_canon_sha256":"628f71eaabebcd7ace7fa98085f2ff724223e96c7e86469c02b8922dd09db949"},"schema_version":"1.0","source":{"id":"2005.00959","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.00959","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"arxiv_version","alias_value":"2005.00959v3","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.00959","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"pith_short_12","alias_value":"6J5HMPDEGPGF","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"pith_short_16","alias_value":"6J5HMPDEGPGFGHOV","created_at":"2026-07-05T03:04:01Z"},{"alias_kind":"pith_short_8","alias_value":"6J5HMPDE","created_at":"2026-07-05T03:04:01Z"}],"graph_snapshots":[{"event_id":"sha256:83315cc59ef3778fc9e3a29109ae17afe3063f718e23c9890f990b212c4102d4","target":"graph","created_at":"2026-07-05T03:04:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2005.00959/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection (BP) based fidelity term as an alternative to the common least squares (LS), and demonstrated excellent results for popular inverse problems. These works have also empirically shown that using the BP term, rather than the LS term, requires fewer iterations of optimization algorithms. In this paper, we examine the convergence rate of the projected gradient d","authors_text":"Raja Giryes, Tom Tirer","cross_cats":["cs.CV","cs.LG","cs.NA","math.NA","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-05-03T00:58:23Z","title":"On the Convergence Rate of Projected Gradient Descent for a Back-Projection based Objective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.00959","kind":"arxiv","version":3},"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":"sha256:5a12c0281a401e77af34385f70ffb02b01569ec548dc42715a86b943532eb94c","target":"record","created_at":"2026-07-05T03:04:01Z","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":"41bcd4d30202d27c4551b6053a8df457472d47429ba5c799dd431107b980c355","cross_cats_sorted":["cs.CV","cs.LG","cs.NA","math.NA","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-05-03T00:58:23Z","title_canon_sha256":"628f71eaabebcd7ace7fa98085f2ff724223e96c7e86469c02b8922dd09db949"},"schema_version":"1.0","source":{"id":"2005.00959","kind":"arxiv","version":3}},"canonical_sha256":"f27a763c6433cc531dd5070869f9111e7eecce262a4a793750c13ee394e6b397","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f27a763c6433cc531dd5070869f9111e7eecce262a4a793750c13ee394e6b397","first_computed_at":"2026-07-05T03:04:01.042858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:04:01.042858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YLoqaS4Rl/3GpoSg0zh+dzL2nJZ/VXtOEuD/1dNxiu0mKQFR0hmvI1Zg8jbRpigxav8TNuUQhpgznzdwjoIGAA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:04:01.043356Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.00959","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a12c0281a401e77af34385f70ffb02b01569ec548dc42715a86b943532eb94c","sha256:83315cc59ef3778fc9e3a29109ae17afe3063f718e23c9890f990b212c4102d4"],"state_sha256":"db68b20f4c692a69fd95f5225378226cca1806f2ca2d9c6cb552c812b489c60e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtnsEOhh1opwOa0Yozgo00xJOMnUPwJucz3qNfDRzLyqZNCeigV28tKJ4dOOjZ2bLHra6itGuGvLlEiZM64JBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T17:20:37.760902Z","bundle_sha256":"749dae3345ac2cdd478b6d2984de07159988fa9fedbb1736eb10406671c877df"}}