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Ptychography, a prevalent imaging technique in fields such as biology andoptics, poses substantial challenges in its reconstruction process,characterized by nonconvexity and large-scale requirements. This paper presentsa novel approach by introducing a class of variational models that incorporatethe weighted difference of anisotropic--isotropic total variation. Thisformulation enables the handling of measurements corrupted by Gaussian orPoisson noise, effectively addressing the nonconvex challenge. To tackle thelarge-scale nature of the problem, we propose an efficient stochasticalternating direction method of multipliers, which guarantees convergence undermild conditions. Numerical experiments validate the superiority of our approachby demonstrating its capability to successfully reconstruct complex-valuedimages, especially in recovering the phase components even in the presence ofhighly corrupted measurements.

A Stochastic ADMM Algorithm for Large-Scale Ptychography with Weighted Difference of Anisotropic and Isotropic Total Variation