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

Ptychography is an imaging technique that has various scientific applications, ranging from biology to optics. The method scans the object of interest in a series of overlapping positions, thereby generating a set of multiple Fourier magnitude measurements that are potentially corrupted by noise. From these measurements, an image of the object can be reconstructed depending on how the related inverse problem is formulated and solved. In this paper, we propose a class of variational models that incorporate the weighted anisotropic--isotropic total variation (AITV), an effective regularizer for image recovery. This class of models is applicable to measurements corrupted by either Gaussian or Poisson noise. In order to have the models applicable for large number of ptychographic scans, we design an efficient stochastic alternating direction method of multipliers algorithm and establish its convergence. Numerical experiments demonstrate that from a large set of highly corrupted Fourier measurements, the proposed stochastic algorithm with AITV regularization can reconstruct complex-valued images with satisfactory quality, especially for the phase components.