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

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.