Solving Blind Ptychography Effectively Via Linearized Alternating Direction Method of Multipliers

The problem of blind ptychography is to determine the specimen object and the scanning probe simultaneously from diffraction data. By formulating the problem as a nonconvex optimization, we propose linearized alternating direction method of multipliers (LADMM) to effectively solve the blind ptychography problem. Different from the iterative ptychographic engines (including ePIE, rPIE and other variants), all of the diffraction patterns are simultaneously exploited in our optimization based approach to address the ill-posedness of the problem. Compared to the existing ADMM-type algorithm in the literature (Chang et al. in SIAM J Imaging Sci 12(1):153–185, 2019), ours is based on a new splitting form for the bilinear term, which enables closed-form solutions for each subproblem. Convergence to stationary point of the considered optimization is provided under certain assumptions. It is observed that the performance of ADMM-type method highly depends on the penalty parameter. Thus LADMM with adaptive penalty parameter is developed to prioritize the reconstruction performance and have empirical convergence guarantee. With numerical comparison to other competitive algorithms, our proposed method outperforms the current state-of-the-art ones on simulated and experimental data, especially for the only limited available diffraction data case, which validates the effectiveness of the proposed algorithm.