An Efficient High-Dimensional Sparse Fourier Transform

We propose RSFT, which is an extension of the one dimensional Sparse Fourier Transform algorithm to higher dimensions in a way that it can be applied to real, noisy data. The RSFT allows for off-grid frequencies. Furthermore, by incorporating Neyman-Pearson detection, the frequency detection stages in RSFT do not require knowledge of the exact sparsity of the signal and are more robust to noise. We analyze the asymptotic performance of RSFT, and study the computational complexity versus the worst case signal SNR tradeoff. We show that by choosing the proper parameters, the optimal tradeoff can be achieved. We discuss the application of RSFT on short range ubiquitous radar signal processing, and demonstrate its feasibility via simulations.