{"paper":{"title":"Sample-Optimal Fourier Sampling in Any Constant Dimension -- Part I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael Kapralov, Piotr Indyk","submitted_at":"2014-03-23T21:39:20Z","abstract_excerpt":"We give an algorithm for $\\ell_2/\\ell_2$ sparse recovery from Fourier measurements using $O(k\\log N)$ samples, matching the lower bound of \\cite{DIPW} for non-adaptive algorithms up to constant factors for any $k\\leq N^{1-\\delta}$. The algorithm runs in $\\tilde O(N)$ time. Our algorithm extends to higher dimensions, leading to sample complexity of $O_d(k\\log N)$, which is optimal up to constant factors for any $d=O(1)$. These are the first sample optimal algorithms for these problems.\n  A preliminary experimental evaluation indicates that our algorithm has empirical sampling complexity compara"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5804","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"}