SAR imaging using the sparse Fourier transform

In wide-bandwidth high-resolution synthetic aperture radar (SAR), high sampling rates generate big demands for computations and storage. This paper exploits the sparsity of the electromagnetic reflectivity of far-field targets in the range-azimuth domain to propose a sparse Fourier transform (SFT) based ranged doppler (RD) algorithm for SAR imaging. The proposed algorithm ensures the same resolution as the RD algorithm with computational complexity O(K log₂ K), where K is of the order of the target scene sparsity, while employing only O(K log₂ N) samples in azimuth direction and O(K log₂ N_t) in range direction, where N and N_t denote the number of Nyquist sampling points in azimuth and range direction, respectively.