  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 ourapproach, 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.
