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We present a sparse multidimensional FFT (sMFFT) randomized algorithm forreal positive vectors. The algorithm works in any fixed dimension, requires(O(R log(R) log(N)) ) samples and runs in O( R log^2(R) log(N)) complexity(where N is the total size of the vector in d dimensions and R is the number ofnonzeros). It is stable to low-level noise and exhibits an exponentially smallprobability of failure.

A sparse multidimensional FFT for real positive vectors