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In this paper, SAR image reconstruction with joint phase error estimation(autofocusing) is formulated as an inverse problem. An optimization modelutilising a sparsity-enforcing Cauchy regularizer is proposed, and analternating minimization framework is used to solve it, in which the desiredimage and the phase errors are optimized alternatively. For the imagereconstruction sub-problem (f-sub-problem), two methods are presented capableof handling the problem's complex nature, and we thus present two variants ofour SAR image autofocusing algorithm. Firstly, we design a complex version ofthe forward-backward splitting algorithm (CFBA) to solve the f-sub-problemiteratively. For the second variant, the Wirtinger alternating minimizationautofocusing (WAMA) method is presented, in which techniques of Wirtingercalculus are utilized to minimize the complex-valued cost function in thef-sub-problem in a direct fashion. For both methods, the phase error estimationsub-problem is solved by simply expanding and observing its cost function.Moreover, the convergence of both algorithms is discussed in detail. Byconducting experiments on both simulated scenes and real SAR images, theproposed method is demonstrated to give impressive autofocusing resultscompared to other state of the art methods.

Sparse regularization with a non-convex penalty for SAR imaging and autofocusing