# Phase retrieval with a multivariate Von Mises prior: from a Bayesian formulation to a lifting solution

## TL;DR

This paper introduces a Bayesian approach for phase retrieval that incorporates prior phase information via a multivariate Von Mises distribution, leading to a lifting optimization solution.

## Contribution

It presents a novel Bayesian formulation for phase retrieval using a multivariate Von Mises prior, connecting it to a lifting optimization method.

## Key findings

- Effective incorporation of phase priors improves retrieval accuracy
- Formulation using Mahalanobis distance enables convex optimization
- Lifting method provides a practical solution for phase recovery

## Abstract

In this paper, we investigate a new method for phase recovery when prior information on the missing phases is available. In particular, we propose to take into account this information in a generic fashion by means of a multivariate Von Mises dis- tribution. Building on a Bayesian formulation (a Maximum A Posteriori estimation), we show that the problem can be expressed using a Mahalanobis distance and be solved by a lifting optimization procedure.