Generalized Proximal Smoothing for Phase Retrieval

TL;DR

The paper introduces the generalized proximal smoothing (GPS) algorithm for phase retrieval that effectively handles noisy data by relaxing constraints and demonstrates superior performance over classical methods in speed, accuracy, and noise robustness.

Contribution

The GPS algorithm is a novel optimization-based approach that relaxes Fourier and object constraints using regularization and smoothing, improving phase retrieval performance.

Findings

GPS outperforms HIO and OSS in convergence speed.

GPS shows higher consistency in phase retrieval results.

GPS demonstrates robustness to noisy data.

Abstract

In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and object constraints. We relax the object constraint by introducing the generalized Moreau-Yosida regularization and heat kernel smoothing. We are able to readily handle the associated proximal mapping in the dual variable by using an infimal convolution. We also relax the magnitude constraint into a least squares fidelity term, whose proximal mapping is available. GPS alternatively iterates between the two proximal mappings in primal and dual spaces, respectively. Using both numerical simulation and experimental data, we show that GPS algorithm consistently outperforms the classical phase retrieval algorithms such as hybrid input-output (HIO) and oversampling smoothness (OSS), in terms of the convergence speed, consistency of the phase retrieval, and robustness to noise.