Fus Florin, Yang Yang, Pacureanu Alexandra, Bohic Sylvain, Cloetens Peter
Opt Express. 2018 Dec 10;26(25):32847-32865. doi: 10.1364/OE.26.032847.
In propagation based phase contrast imaging, intensity patterns are recorded on a x-ray detector at one or multiple propagation distances, called in-line holograms. They form the input of an inversion algorithm that aims at retrieving the phase shift induced by the object. The problem of phase retrieval in in-line holography is an ill-posed inverse problem. Consequently an adequate solution requires some form of regularization with the most commonly applied being the classical Tikhonov regularization. While generally satisfying this method suffers from a few issues such as the choice of the regularization parameter. Here, we offer an alternative to the established method by applying the principles of Bayesian inference. We construct an iterative optimization algorithm capable of both retrieving the unknown phase and determining a multi-dimensional regularization parameter. In the end, we highlight the advantages of the introduced algorithm, chief among them being the unsupervised determination of the regularization parameter(s). The proposed approach is tested on both simulated and experimental data and is found to provide robust solutions, with improved response to typical issues like low frequency noise and the twin-image problem.
在基于传播的相衬成像中，强度图案在一个或多个传播距离处记录在X射线探测器上，称为同轴全息图。它们构成了旨在检索由物体引起的相移的反演算法的输入。同轴全息术中的相位恢复问题是一个不适定的逆问题。因此，一个合适的解决方案需要某种形式的正则化，最常用的是经典的蒂霍诺夫正则化。虽然该方法总体上令人满意，但它存在一些问题，如正则化参数的选择。在这里，我们通过应用贝叶斯推理原理提供了一种替代现有方法的方法。我们构建了一种迭代优化算法，能够同时检索未知相位并确定多维正则化参数。最后，我们强调了所引入算法的优点，其中主要优点是正则化参数的无监督确定。所提出的方法在模拟数据和实验数据上都进行了测试，发现它能提供稳健的解决方案，对低频噪声和双像问题等典型问题的响应有所改善。
