Undersampled Phase Retrieval via Majorization-Minimization

TL;DR

This paper introduces low-complexity algorithms based on majorization-minimization for undersampled phase retrieval, exploiting sparsity to improve recovery from fewer measurements with higher accuracy.

Contribution

It develops novel MM-based algorithms that outperform existing methods in undersampled phase retrieval by leveraging signal sparsity and providing simple, monotonic optimization steps.

Findings

Algorithms outperform benchmarks in recovery probability.

Methods achieve higher accuracy with fewer measurements.

Experiments validate superior performance over existing approaches.

Abstract

In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce the number of required measurements since a recent theory established that $M\approx4N$ intensity measurements are necessary and sufficient to recover a generic signal $\mathbf{x}$. In this paper, we propose to exploit the sparsity in the original signal and develop low-complexity algorithms with superior performance based on the majorization-minimization (MM) framework. The proposed algorithms 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. Experimental results validate that our algorithms outperform existing up-to-date methods in terms of recovery probability and accuracy, under the same settings.