{"paper":{"title":"An Adaptive Sublinear-Time Block Sparse Fourier Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amir Zandieh, Jonathan Scarlett, Michael Kapralov, Volkan Cevher","submitted_at":"2017-02-04T13:31:47Z","abstract_excerpt":"The problem of approximately computing the $k$ dominant Fourier coefficients of a vector $X$ quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in algorithms with $O(k\\log n\\log (n/k))$ runtime [Hassanieh et al., STOC'12] and $O(k\\log n)$ sample complexity [Indyk et al., FOCS'14]. These results are proved using non-adaptive algorithms, and the latter $O(k\\log n)$ sample complexity result is essentially the best possible under the sparsity assumption alone.\n  This paper revisits the spa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01286","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"}