{"paper":{"title":"Batch Sparse Recovery, or How to Leverage the Average Sparsity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexandr Andoni, Eric Price, Lior Kamma, Robert Krauthgamer","submitted_at":"2018-07-23T08:31:23Z","abstract_excerpt":"We introduce a \\emph{batch} version of sparse recovery, where the goal is to report a sequence of vectors $A_1',\\ldots,A_m' \\in \\mathbb{R}^n$ that estimate unknown signals $A_1,\\ldots,A_m \\in \\mathbb{R}^n$ using a few linear measurements, each involving exactly one signal vector, under an assumption of \\emph{average sparsity}. More precisely, we want to have \\newline\n  $(1) \\;\\;\\; \\sum_{j \\in [m]}{\\|A_j- A_j'\\|_p^p} \\le C \\cdot \\min \\Big\\{ \\sum_{j \\in [m]}{\\|A_j - A_j^*\\|_p^p} \\Big\\}$\n  for predetermined constants $C \\ge 1$ and $p$, where the minimum is over all $A_1^*,\\ldots,A_m^*\\in\\mathbb{R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08478","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":""},"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"}