Deterministic sampling of sparse trigonometric polynomials
Journal of Complexity
Simple and practical algorithm for sparse Fourier transform
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Nearly optimal sparse fourier transform
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions
SIAM Journal on Matrix Analysis and Applications
Strengthening hash families and compressive sensing
Journal of Discrete Algorithms
Sketching via hashing: from heavy hitters to compressed sensing to sparse fourier transform
Proceedings of the 32nd symposium on Principles of database systems
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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 $\hat{\mathbf{A}}$, 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 (Gilbert et al. in ACM STOC, pp. 152–161, 2002; Proceedings of SPIE Wavelets XI, 2005). 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 (Gilbert et al. in Proceedings of SPIE Wavelets XI, 2005). Finally, the Fourier algorithm we develop here implies a simpler optimized version of the deterministic compressed sensing method previously developed in (Iwen in Proc. of ACM-SIAM Symposium on Discrete Algorithms (SODA’08), 2008).