(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 -sparse approximation to the -dimensional Fourier transform of a length signal. Our algorithm uses samples, is dimension-free, operates for any universe size, and achieves the strongest 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.
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}
}