Solving Phase Retrieval with a Learned Reference

Abstract

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by leveraging some prior knowledge about the structure of the unknown image. The inherent ambiguities about shift and flip in the Fourier measurements make this problem especially difficult; and most of the existing methods use several random restarts with different permutations. In this paper, we assume that a known (learned) reference is added to the signal before capturing the Fourier amplitude measurements. Our method is inspired by the principle of adding a reference signal in holography. To recover the signal, we implement an iterative phase retrieval method as an unrolled network. Then we use back propagation to learn the reference that provides us the best reconstruction for a fixed number of phase retrieval iterations. We performed a number of simulations on a variety of datasets under different conditions and found that our proposed method for phase retrieval via unrolled network and learned reference provides near-perfect recovery at fixed (small) computational cost. We compared our method with standard Fourier phase retrieval methods and observed significant performance enhancement using the learned reference.

DeepPhaseCut: Deep Relaxation in Phase for Unsupervised Fourier Phase Retrieval

“…In the first category, a pretrained network is employed as a regularization or prior for the reconstruction [19], [20], [24]. Specifically, in [19], a pretrained network for the denoising task serves as a regularization when exploiting the regularization-bydenoising (RED) framework to solve the phase retrieval problem.…”

“…Hand et al [20] proposed generative prior from a pretrained generative model to restore phase information. In [24], the reference provided by the trained network was exploited as a prior during the reconstruction process. Although leveraging the knowledge from the pretrained network leads to a better reconstruction quality, the optimization problems defined in these algorithms have to be solved in an iterative manner.…”

“…Recently, various forms of deep learning approaches have been investigated as a fast and effective approach for phase retrieval [19], [20], [21], [22], [23], [24], [25], [26]. All of these algorithms have demonstrated high performance compared to the traditional alternating projection-based methods.…”