Combinatorial Sublinear-Time Fourier Algorithms

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Combinatorial Sublinear-Time Fourier Algorithms
We study the problem of estimating the best k term Fourier representation for a given frequency-sparse signal (i.e., vector) A of length N k. More explicitly, we investigate how to deterministically identify k of the largest magnitude frequencies of ˆA, and estimate their coefficients, in polynomial(k, log N) time. Randomized sublinear time algorithms which have a small (controllable) probability of failure for each processed signal exist for solving this problem [24, 25]. In this paper we develop the first known deterministic sublinear time sparse Fourier Transform algorithm which is guaranteed to produce accurate results. As an added bonus, a simple relaxation of our deterministic Fourier result leads to a new Monte Carlo Fourier algorithm with similar runtime/sampling bounds to the current best randomized Fourier method [25]. Finally, the Fourier algorithm we develop here implies a simpler optimized version of the deterministic compressed sensing method previously developed in [...
Mark A. Iwen
Added 25 Jan 2011
Updated 25 Jan 2011
Type Journal
Year 2010
Where FOCM
Authors Mark A. Iwen
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