Overlapping Domain Decomposition Methods for Ptychographic Imaging

In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge amount of frames are generated, and thus it poses a great demand of parallel computing in order to solve this large-scale inverse problem. In this paper, we propose the overlapping Domain Decomposition Methods (DDMs) to solve the nonconvex optimization problem in ptychographic imaging, that decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information on the interface of these subdomains, thus leading to highly parallel algorithms with good load balance. More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping region for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric. Then the Alternating Direction Method of Multipliers (ADMM) is utilized to generate an efficient Overlapping Domain Decomposition based Ptychography algorithm (OD2P) for the two-subdomain domain decomposition (DD), where all subproblems can be computed with close-form solutions. Due to the Lipschitz continuity for the gradient of the objective function, the convergence of the proposed OD2P is derived under mild conditions. Moreover, it is extended to more general case including multiple-subdomain DD and blind recovery. Numerical experiments are further conducted to show the performance of proposed algorithms, demonstrating good convergence speed and robustness to the noise. Especially, we report the virtual wall-clock time of proposed algorithm, which shows great potential for parallel computing in massively parallel processing computers.