标题： 相位恢复的邻近算子 显示英文标题

标题： Proximity Operators for Phase Retrieval

摘要： 我们提出了一种新的邻近算子族的表述，这些邻近算子推广了相位检索中的投影步骤。 这些针对噪声强度测量的邻近算子可以替换任何基于投影的算法中的经典“无噪声”投影。 它们来源于最大似然公式，并且对于高斯和泊松情况都具有闭式解。 此外，我们将这些邻近算子扩展到欠采样强度测量。 为了评估它们的性能，这些算子被应用于经典的Gerchberg Saxton算法中。 我们展示了数值实验，结果表明使用这些邻近算子重建的复振幅始终优于使用经典强度投影，而其计算开销是适度的。 显示英文摘要

摘要： We present a new formulation of a family of proximity operators that generalize the projector step for phase retrieval. These proximity operators for noisy intensity measurements can replace the classical "noise free" projection in any projection-based algorithm. They are derived from a maximum likelihood formulation and admit closed form solutions for both the Gaussian and the Poisson cases. In addition, we extend these proximity operators to undersampled intensity measurements. To assess their performance, these operators are exploited in a classical Gerchberg Saxton algorithm. We present numerical experiments showing that the reconstructed complex amplitudes with these proximity operators perform always better than using the classical intensity projector while their computational overhead is moderate.