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arXiv · 1909.11123

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

Vasileios Nakos·Zhao Song·Zhengyu Wang
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Abstract

In this paper, we consider the extensively studied problem of computing a $k$-sparse approximation to the $d$-dimensional Fourier transform of a length $n$ signal. Our algorithm uses $O(k \log k \log n)$ samples, is dimension-free, operates for any universe size, and achieves the strongest $\ell_\infty/\ell_2$ 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.

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Vasileios Nakos, Zhao Song, Zhengyu Wang. 2019-09-24. (Nearly) Sample-Optimal Sparse Fourier Transform in Any Dimension; RIPless and Filterless. https://arxiv.org/abs/1909.11123

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