(Nearly) Sample-Optimal Sparse Fourier Transform
نویسندگان
چکیده
We consider the problem of computing a k-sparse approximation to the discrete Fourier transform of an n-dimensional signal. Our main result is a randomized algorithm that computes such an approximation using O(k log n(log log n)) signal samples in time O(k log n(log log n)), assuming that the entries of the signal are polynomially bounded. The sampling complexity improves over the recent bound of O(k log n log(n/k)) given in [HIKP12b], and matches the lower bound of Ω(k log(n/k)/ log log n) from the same paper up to poly(log log n) factors when k = O(n1−δ) for a constant δ > 0. ∗We acknowledge financial support from grant #FA9550-12-1-0411 from the U.S. Air Force Office of Scientific Research (AFOSR) and the Defense Advanced Research Projects Agency (DARPA).
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