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(Nearly) Sample-Optimal Sparse Fourier Transform in Any Dimension; RIPless and Filterless (1909.11123v1)
Published 24 Sep 2019 in cs.DS, cs.IT, and math.IT
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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