Solving Phase Retrieval with a Learned Reference

TL;DR

This paper introduces a novel phase retrieval method that learns a reference signal to improve Fourier image reconstruction, achieving near-perfect results with fixed computational effort.

Contribution

It proposes an unrolled network approach that learns an optimal reference signal for Fourier phase retrieval, enhancing accuracy over traditional methods.

Findings

Significant performance improvement over standard methods.

Near-perfect image recovery with fixed small number of iterations.

Effective learning of reference signals for phase retrieval.

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.