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.

翻译：叠层成像作为一种广泛应用于生物学和光学领域的成像技术，其重建过程面临非凸性和大规模计算需求的重大挑战。本文提出一种创新方法，通过引入含各向异性-各向同性全变分加权差的变分模型族，该模型能有效处理受高斯或泊松噪声污染的测量数据，并成功解决非凸优化难题。针对问题的大规模特性，我们提出一种高效随机交替方向乘子法，该算法在温和条件下保证收敛性。数值实验验证了本方法的优越性，证明其能够成功重建复值图像，尤其在高度污染的测量数据中仍能有效恢复相位成分。