Accelerated Image Reconstruction for Nonlinear Diffractive Imaging

The radar autofocus problem arises in situations where radar measurements are acquired of a scene using antennas that suffer from position ambiguity. Current techniques model the antenna ambiguity as a global phase error affecting the received radar measurement at every antenna. However, the phase error signal model is only valid in the far field regime where the position error can be approximated by a one dimensional shift in the down-range direction. We propose in this paper an alternate formulation where the antenna position error is modeled using a two-dimensional shift operator in the imagedomain. The radar autofocus problem then becomes a multichannel two-dimensional blind deconvolution problem where the static radar image is convolved with a two dimensional shift kernel for each antenna measurement. We develop an alternating minimization framework that leverages the sparsity and piece-wise smoothness of the radar scene, as well as the one-sparse property of the two dimensional shift kernels.