Phase recovery from a Bayesian point of view: the variational approach

TL;DR

This paper introduces a Bayesian variational method for phase recovery, deriving an iterative algorithm that efficiently estimates complex signals from magnitude measurements, demonstrating robustness and computational efficiency on synthetic data.

Contribution

It presents a novel variational Bayesian approach with an iterative algorithm for phase recovery, under the mean-field assumption, improving robustness and efficiency.

Findings

Effective phase recovery on synthetic data

Algorithm exhibits robustness to noise

Computational cost is manageable

Abstract

In this paper, we consider the phase recovery problem, where a complex signal vector has to be estimated from the knowledge of the modulus of its linear projections, from a naive variational Bayesian point of view. In particular, we derive an iterative algorithm following the minimization of the Kullback-Leibler divergence under the mean-field assumption, and show on synthetic data with random projections that this approach leads to an efficient and robust procedure, with a good computational cost.