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

TL;DR

This paper introduces a stochastic ADMM algorithm for large-scale ptychography that effectively reconstructs complex images with noisy measurements by leveraging a novel variational model involving weighted anisotropic and isotropic total variation.

Contribution

It proposes a new variational model and a stochastic ADMM algorithm that together improve reconstruction quality and efficiency in large-scale, noisy ptychography problems.

Findings

Successfully reconstructs complex-valued images with high accuracy.

Effectively handles measurements corrupted by Gaussian or Poisson noise.

Demonstrates convergence and superior performance through numerical experiments.

Abstract

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.