  Ptychography, a prevalent imaging technique in fields such as biology and
optics, poses substantial challenges in its reconstruction process,
characterized by nonconvexity and large-scale requirements. This paper presents
a novel approach by introducing a class of variational models that incorporate
the weighted difference of anisotropic--isotropic total variation. This
formulation enables the handling of measurements corrupted by Gaussian or
Poisson noise, effectively addressing the nonconvex challenge. To tackle the
large-scale nature of the problem, we propose an efficient stochastic
alternating direction method of multipliers, which guarantees convergence under
mild conditions. Numerical experiments validate the superiority of our approach
by demonstrating its capability to successfully reconstruct complex-valued
images, especially in recovering the phase components even in the presence of
highly corrupted measurements.
