Deep iterative reconstruction for phase retrieval

The classical phase retrieval problem is the recovery of a constrained image from the magnitude of its Fourier transform. Although there are several well-known phase retrieval algorithms, including the hybrid input-output (HIO) method, the reconstruction performance is generally sensitive to initialization and measurement noise. Recently, deep neural networks (DNNs) have been shown to provide state-of-the-art performance in solving several inverse problems such as denoising, deconvolution, and superresolution. In this work, we develop a phase retrieval algorithm that utilizes two DNNs together with the model-based HIO method. First, a DNN is trained to remove the HIO artifacts, and is used iteratively with the HIO method to improve the reconstructions. After this iterative phase, a second DNN is trained to remove the remaining artifacts. Numerical results demonstrate the effectiveness of our approach, which has little additional computational cost compared to the HIO method. Our approach not only achieves state-of-the-art reconstruction performance but also is more robust to different initialization and noise levels.