English

(Nearly) Sample-Optimal Sparse Fourier Transform in Any Dimension; RIPless and Filterless

Data Structures and Algorithms 2019-09-26 v1 Information Theory math.IT

Abstract

In this paper, we consider the extensively studied problem of computing a kk-sparse approximation to the dd-dimensional Fourier transform of a length nn signal. Our algorithm uses O(klogklogn)O(k \log k \log n) samples, is dimension-free, operates for any universe size, and achieves the strongest /2\ell_\infty/\ell_2 guarantee, while running in a time comparable to the Fast Fourier Transform. In contrast to previous algorithms which proceed either via the Restricted Isometry Property or via filter functions, our approach offers a fresh perspective to the sparse Fourier Transform problem.

Keywords

Cite

@article{arxiv.1909.11123,
  title  = {(Nearly) Sample-Optimal Sparse Fourier Transform in Any Dimension; RIPless and Filterless},
  author = {Vasileios Nakos and Zhao Song and Zhengyu Wang},
  journal= {arXiv preprint arXiv:1909.11123},
  year   = {2019}
}
R2 v1 2026-06-23T11:24:44.698Z