PRIME: Phase Retrieval via Majorization-Minimization

TL;DR

PRIME introduces low-complexity algorithms for phase retrieval using majorization-minimization, achieving superior recovery performance and lower mean square error compared to existing methods.

Contribution

The paper develops four novel algorithms based on MM for phase retrieval, offering a simple, closed-form solution at each iteration with improved accuracy.

Findings

Outperforms benchmark methods in successful recovery.

Achieves lower mean square error across various settings.

Monotonically decreases the objective function during iterations.

Abstract

This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with superior performance based on the majorization-minimization (MM) framework. The proposed algorithms are referred to as PRIME: Phase Retrieval vIa the Majorization-minimization techniquE. They are preferred to existing benchmark methods since at each iteration a simple surrogate problem is solved with a closed-form solution that monotonically decreases the original objective function. In total, four algorithms are proposed using different majorization-minimization techniques. Experimental results validate that our algorithms outperform existing methods in terms of successful recovery and mean square error under various settings.