  In this paper, an optimization model using Cauchy regularization is proposed
for simultaneous SAR image reconstruction and autofocusing. A coordinate
descent framework in which the desired image and the phase errors are optimized
alternatively is designed to solve the model. For the subproblem of estimating
the image, we utilize the techniques of Wirtinger calculus to directly minimize
the cost function which involves complex variables. We also utilise a
state-of-the-art, sparsity-enforcing Cauchy regularizer. The proposed method is
demonstrated to give impressive autofocusing results by conducting experiments
on both simulated scene and real SAR image.
