{"paper":{"title":"Accelerated Exact Recovery from Noisy Data via Averaging and Noise-Aware Adaptive Bregman-Kaczmarz","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Abakar A. Mahamat, Idriss Tondji, Lionel Tondji","submitted_at":"2026-07-17T14:39:17Z","abstract_excerpt":"The adaptive Bregman-Kaczmarz method recovers the exact, noise-free solution of a linear inverse problem even when every measurement it queries is corrupted, provided the corruption is fresh, independent and zero-mean. A block version was proposed for parallel hardware, but whether larger blocks actually converge faster was left open. We show the answer hinges on how the block is used: replacing the block sum with a block average collapses the analysis onto a single positive-semidefinite matrix, through which we prove that the guaranteed convergence improves monotonically with the batch size, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16003/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"}