This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is placed on the connections between the numerous alternating projections strategies derived from Fienup's phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup's algorithm as iterates of a proximal gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projections techniques to the inverse problems formulation is straightforward and advantageous.

中文翻译：

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从Fienup的相位检索技术到在线全息术的正则化反演：教程。

本文包括一个有关如何使用逆问题方法重建在线全息图的教程，该教程将从对观察结果进行建模，选择正则化和约束条件开始，然后到重建算法的设计结束。特别关注的是Fienup的相位检索技术衍生的众多交替投影策略与逆问题框架之间的联系。特别是，给出了Fienup算法的解释，即针对特定成本函数迭代近端梯度下降。从测微珠的模拟全息图和实验全息图重建的图像说明了理论发展。结果表明，从交替投影技术到反问题公式的过渡是直接且有利的。