Convex Augmentation for Total Variation Based Phase Retrieval

TL;DR

This paper proposes a convex augmentation method using total variation regularization for phase retrieval with noisy measurements, offering an efficient algorithm with proven convergence and demonstrated effectiveness through experiments.

Contribution

It introduces a novel convex augmentation model for phase retrieval that is more flexible and efficiently solvable than existing methods like PhaseLift.

Findings

Effective in noisy measurement scenarios

Converges reliably with the modified sPADMM

Outperforms some existing methods in experiments

Abstract

Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a convex augmentation approach for phase retrieval based on total variation regularization. In contrast to popular convex relaxation models like PhaseLift, our model can be efficiently solved by a modified semi-proximal alternating direction method of multipliers (sPADMM). The modified sPADMM is more general and flexible than the standard one, and its convergence is also established in this paper. Extensive numerical experiments are conducted to showcase the effectiveness of the proposed method.