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

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 distribution. 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.