Robust contrast-transfer-function phase retrieval via flexible deep learning networks

By exploiting the total variation (TV) regularization scheme and the contrast transfer function (CTF), a phase map can be retrieved from single-distance coherent diffraction images via the sparsity of the investigated object. However, the CTF-TV phase retrieval algorithm often struggles in the presence of strong noise, since it is based on the traditional compressive sensing optimization problem. Here, convolutional neural networks, a powerful tool from machine learning, are used to regularize the CTF-based phase retrieval problems and improve the recovery performance. This proposed method, the CTF-Deep phase retrieval algorithm, was tested both via simulations and experiments. The results show that it is robust to noise and fast enough for high-resolution applications, such as in optical, x-ray, or terahertz imaging.