Alternating Phase Langevin Sampling with Implicit Denoiser Priors for Phase Retrieval

TL;DR

This paper introduces an innovative phase retrieval method that leverages implicit denoiser priors within an alternating minimization framework, achieving competitive results especially on out-of-distribution images.

Contribution

It proposes a novel approach combining denoiser priors with classical optimization for phase retrieval, enhancing performance on diverse image distributions.

Findings

Competitive performance on Fourier measurements

Improved results on out-of-distribution images

Effective integration of denoiser priors in optimization

Abstract

Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is highly ill-posed due to the phase-induced ambiguities and the large number of possible images that can fit to the given measurements. Thus, there's a rich history of enforcing structural priors to improve solutions including sparsity priors and deep-learning-based generative models. However, such priors are often limited in their representational capacity or generalizability to slightly different distributions. Recent advancements in using denoisers as regularizers for non-convex optimization algorithms have shown promising performance and generalization. We present a way of leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical alternating minimization framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with Fourier measurements on in-distribution images and notable improvement on out-of-distribution images.