Wirtinger梯度下降方法用于低剂量泊松相位检索
Wirtinger gradient descent methods for low-dose Poisson phase retrieval
AI总结：
针对光学成像中低剂量泊松噪声主导的相位检索问题，基于泊松最大对数似然函数设计并分析了保证收敛与损失下降的Wirtinger梯度下降算法，数值实验验证了其有效性。
摘要：
相位检索问题在光学成像领域有许多应用。受生物样本成像实验的启发，我们主要考虑泊松噪声起主导作用的低剂量照明设置。本文讨论了基于不同损失函数的梯度下降算法，这些损失函数适用于受泊松噪声影响的数据，特别是在低剂量情况下。从泊松分布的最大对数似然函数出发，我们研究了该问题的不同正则化和近似，以设计出满足应用中面临要求的算法。在此过程中，我们重点关注低计数测量。对于所有建议的损失函数，我们研究了相应梯度下降算法到驻点的收敛性，并找到了保证每次迭代中损失下降的固定步长。在低剂量情况下进行了数值实验，以证实理论观察结果。
英文摘要：
The problem of phase retrieval has many applications in the field of optical imaging. Motivated by imaging experiments with biological specimens, we primarily consider the setting of low-dose illumination where Poisson noise plays the dominant role. In this paper, we discuss gradient descent algorithms based on different loss functions adapted to data affected by Poisson noise, in particular in the low-dose regime. Starting from the maximum log-likelihood function for the Poisson distribution, we investigate different regularizations and approximations of the problem to design an algorithm that meets the requirements that are faced in applications. In the course of this, we focus on low-count measurements. For all suggested loss functions, we study the convergence of the respective gradient descent algorithms to stationary points and find constant step sizes that guarantee descent of the loss in each iteration. Numerical experiments in the low-dose regime are performed to corroborate the theoretical observations.
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