SIAM Journal on Scientific Computing, Volume 43, Issue 3, Page B570-B597, January 2021.
In ptychography experiments, redundant scanning is usually required to guarantee the stable recovery, such that a huge number of frames are generated, and thus it poses a great demand on parallel computing to solve this large-scale inverse problem. In this paper, we propose the overlapping domain decomposition methods to solve the nonconvex optimization problem in ptychographic imaging. They decouple the problem defined on the whole domain into subproblems only defined on the subdomains with synchronizing information in the overlapping regions of these subdomains, thus leading to highly parallel algorithms with good load balance. More specifically, for the nonblind recovery (with known probe in advance), by enforcing the continuity of the overlapping regions for the image (sample), the nonlinear optimization model is established based on a novel smooth-truncated amplitude-Gaussian metric (ST-AGM). Such a metric allows for fast calculation of the proximal mapping with closed form, and meanwhile provides the possibility for the convergence guarantee of the first-order nonconvex optimization algorithm due to its Lipschitz smoothness. Then the alternating direction method of multipliers is utilized to generate an efficient overlapping domain decomposition based ptychography algorithm (OD${}^2$P) for the two-subdomain domain decomposition (DD), where all subproblems can be computed with closed-form solutions. Due to the Lipschitz continuity for the gradient of the objective function with ST-AGM, the convergence of the proposed OD${}^2$P is derived under mild conditions. Moreover, it is extended to more general cases including multiple-subdomain DD and blind recovery. Numerical experiments are further conducted to show the performance of proposed algorithms, demonstrating good convergence speed and robustness to the noise. Especially, we report the virtual wall-clock time of proposed algorithm up to 10 processors, which shows potential for upcoming massively parallel computations.

中文翻译：

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谱图成像的重叠域分解方法

SIAM科学计算杂志，第43卷，第3期，第B570-B597页，2021年1月。
在密码术实验中，通常需要冗余扫描以确保稳定的恢复，从而生成大量帧，因此，对于解决该大规模逆问题的并行计算提出了很高的要求。在本文中，我们提出了重叠域分解方法，以解决声像图成像中的非凸优化问题。它们将整个域中定义的问题分解为仅在子域中定义的子问题，并在这些子域的重叠区域中同步信息，从而导致具有良好负载平衡的高度并行算法。更具体地说，对于非盲恢复（预先使用已知的探头），通过对图像（样本）的重叠区域实施连续性，基于一种新的平滑截断幅度高斯度量（ST-AGM），建立了非线性优化模型。这种度量允许以封闭形式快速计算近端贴图，同时由于其Lipschitz平滑性而为一阶非凸优化算法的收敛保证提供了可能性。然后利用乘数的交替方向方法为两子域域分解（DD）生成有效的基于重叠域分解的密码算法（OD $ {} ^ 2 $ P），其中所有子问题都可以采用闭式计算解决方案。由于具有ST-AGM的目标函数梯度的Lipschitz连续性，因此建议的OD $ {} ^ 2 $ P的收敛是在温和条件下得出的。而且，它扩展到更一般的情况，包括多子域DD和盲目恢复。进一步进行了数值实验，以证明所提出算法的性能，证明了良好的收敛速度和对噪声的鲁棒性。特别是，我们报告了所建议算法的虚拟挂钟时间，最多可容纳10个处理器，这表明了即将进行的大规模并行计算的潜力。