Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximation

TL;DR

This paper introduces deepECpr, a novel phase retrieval method combining expectation-consistent approximation with deep denoising networks, achieving faster and more accurate image recovery from phaseless measurements than existing methods.

Contribution

It presents a new approach that integrates EC approximation with deep denoising and a stochastic damping scheme, requiring fewer denoiser calls and outperforming state-of-the-art techniques.

Findings

Improves PSNR and SSIM over existing methods.

Requires fewer denoiser calls for similar or better accuracy.

Effective on various measurement types and image datasets.

Abstract

Accurately recovering images from phaseless measurements is a challenging and long-standing problem. In this work, we present "deepECpr," which combines expectation-consistent (EC) approximation with deep denoising networks to surpass state-of-the-art phase-retrieval methods in both speed and accuracy. In addition to applying EC in a non-traditional manner, deepECpr includes a novel stochastic damping scheme that is inspired by recent diffusion methods. Like existing phase-retrieval methods based on plug-and-play priors, regularization by denoising, or diffusion, deepECpr iterates a denoising stage with a measurement-exploitation stage. But unlike existing methods, deepECpr requires far fewer denoiser calls. We compare deepECpr to the state-of-the-art prDeep (Metzler et al., 2018), Deep-ITA (Wang et al., 2020), DOLPH (Shoushtari et al., 2023), and Diffusion Posterior Sampling (Chung et al., 2023) methods for noisy phase-retrieval of color, natural, and unnatural grayscale images on oversampled-Fourier and coded-diffraction-pattern measurements and find improvements in both PSNR and SSIM with significantly fewer denoiser calls.