{"paper":{"title":"Lower Bounds for Sparse Recovery","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DS","authors_text":"David P. Woodruff, Eric Price, Khanh Do Ba, Piotr Indyk","submitted_at":"2011-06-02T05:20:14Z","abstract_excerpt":"We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying\n  ||x-x'||_1 <= C min_{k-sparse} x\"} ||x-x\"||_1.\n  It is known that there exist matrices A with this property that have only O(k log (n/k)) rows.\n  In this paper we show that this bound is tight. Our bound holds even for the more general /randomized/ version of the problem, where A is a random variable and the recovery algorithm is required to work for any fixed x with constant probability (over A)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0365","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"}