Fast Fourier transforms for nonequispaced data
SIAM Journal on Scientific Computing
Learning decision trees using the Fourier spectrum
SIAM Journal on Computing
Randomized Interpolation and Approximationof Sparse Polynomials
SIAM Journal on Computing
Near-optimal sparse fourier representations via sampling
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Proving Hard-Core Predicates Using List Decoding
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
One sketch for all: fast algorithms for compressed sensing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Foundations of Computational Mathematics
Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
Foundations of Computational Mathematics
Combinatorial Sublinear-Time Fourier Algorithms
Foundations of Computational Mathematics
Combinatorial algorithms for compressed sensing
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
IEEE Transactions on Information Theory
Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
IEEE Transactions on Information Theory
On the Design of Deterministic Matrices for Fast Recovery of Fourier Compressible Functions
SIAM Journal on Matrix Analysis and Applications
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We study the problem of quickly estimating the best k-term Fourier representation for a given periodic function f: [0, 2驴] 驴 驴. Solving this problem requires the identification of k of the largest magnitude Fourier series coefficients of f in worst case k 2 · log O(1) N time. Randomized sublinear-time Monte Carlo algorithms, which have a small probability of failing to output accurate answers for each input signal, have been developed for solving this problem (Gilbert et al. 2002, 2005). These methods were implemented as the Ann Arbor Fast Fourier Transform (AAFFT) and empirically evaluated in Iwen et al. (Commun Math Sci 5(4):981---998, 2007). In this paper we present a new implementation, called the Gopher Fast Fourier Transform (GFFT), of more recently developed sparse Fourier transform techniques (Iwen, Found Comput Math 10(3):303---338, 2010, Appl Comput Harmon Anal, 2012). Experiments indicate that GFFT is faster than AAFFT. In addition to our empirical evaluation, we also consider the existence of sublinear-time Fourier approximation methods with deterministic approximation guarantees for functions whose sequences of Fourier series coefficents are compressible. In particular, we prove the existence of sublinear-time Las Vegas Fourier Transforms which improve on the recent deterministic Fourier approximation results of Iwen (Found Comput Math 10(3):303---338, 2010, Appl Comput Harmon Anal, 2012) for Fourier compressible functions by guaranteeing accurate answers while using an asymptotically near-optimal number of function evaluations.