PhaseLin: Linear Phase Retrieval

TL;DR

PhaseLin introduces a simple linear algorithm for phase retrieval that, with an initial guess, achieves competitive performance and allows for precise MSE analysis, improving efficiency over existing methods.

Contribution

The paper presents PhaseLin, a linear estimator for phase retrieval that simplifies the process and enables exact MSE analysis, outperforming or matching current methods.

Findings

PhaseLin performs on par with existing phase retrieval algorithms.

Exact MSE analysis is possible for arbitrary measurement matrices.

Iterative use of PhaseLin enhances performance effectively.

Abstract

Phase retrieval deals with the recovery of complex- or real-valued signals from magnitude measurements. As shown recently, the method PhaseMax enables phase retrieval via convex optimization and without lifting the problem to a higher dimension. To succeed, PhaseMax requires an initial guess of the solution, which can be calculated via spectral initializers. In this paper, we show that with the availability of an initial guess, phase retrieval can be carried out with an ever simpler, linear procedure. Our algorithm, called PhaseLin, is the linear estimator that minimizes the mean squared error (MSE) when applied to the magnitude measurements. The linear nature of PhaseLin enables an exact and nonasymptotic MSE analysis for arbitrary measurement matrices. We furthermore demonstrate that by iteratively using PhaseLin, one arrives at an efficient phase retrieval algorithm that performs on par with existing convex and nonconvex methods on synthetic and real-world data.