SIAM Journal on Imaging Sciences, Volume 13, Issue 2, Page 609-650, January 2020.
Douglas--Rachford splitting (DRS) methods based on the proximal point algorithms for the Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase retrieval. Fixed point analysis shows that the DRS iterated sequences are always bounded explicitly in terms of the step size and that the fixed points are attracting if and only if the fixed points are regular solutions. This alleviates two major drawbacks of the classical Douglas--Rachford algorithm: slow convergence when the feasibility problem is consistent and divergent behavior when the feasibility problem is inconsistent. Fixed point analysis also leads to a simple, explicit expression for the optimal step size in terms of the spectral gap of an underlying matrix. When applied to the challenging problem of blind ptychography, which seeks to recover both the object and the probe simultaneously, alternating minimization with the DRS inner loops, even with a far from optimal step size, converges geometrically under the nearly minimum conditions established in the uniqueness theory.

中文翻译：

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Douglas-Rachford分割的固定点分析，用于色谱分析和相位检索

SIAM影像科学杂志，第13卷，第2期，第609-650页，2020年1月。
提出了基于近点算法的泊松和高斯对数似然函数的道格拉斯-拉福德分裂（DRS）方法，用于谱图和相位检索。定点分析表明，DRS迭代序列始终在步长方面明确限制，并且当且仅当固定点是正则解时，固定点才吸引。这缓解了经典Douglas-Rachford算法的两个主要缺点：可行性问题一致时收敛速度慢，可行性问题不一致时行为发散。定点分析还可以根据基础矩阵的光谱间隙对最佳步长进行简单，明确的表达。当应用于盲目密码术的挑战性问题时，