Sparse 2D Fast Fourier Transform

This paper extends the concepts of the Sparse Fast Fourier Transform (sFFT) Algorithm introduced in [1] to work with two dimensional (2D) data. The 2D algorithm requires several generalizations to multiple key concepts of the 1D sparse Fourier transform algorithm. Furthermore, several parameters needed in the algorithm are optimized for the reconstruction of sparse image spectra. This paper addresses the case of the exact k-sparse Fourier transform but the underlying concepts can be applied to the general case of finding a k-sparse approximation of the Fourier transform of an arbitrary signal. The proposed algorithm can further be extended to even higher dimensions. Simulations illustrate the efficiency and accuracy of the proposed algorithm when applied to real images.