An adaptive sublinear-time block sparse fourier transform

Abstract

The problem of approximately computing the k dominant Fourier coefficients of a vector X quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in algorithms with O(klognlog(n/k)) runtime [Hassanieh et al., STOC'12] and O(klogn) sample complexity [Indyk et al., FOCS'14]. This paper revisits the sparse FFT problem with the added twist that the sparse coefficients approximately obey a (k0,k1)-block sparse model. In this model, signal frequencies are clustered in k0 intervals with width k1 in Fourier space, and k= k0k1 is the total sparsity.