Face frontalization consists of synthesizing a frontally-viewed face from an arbitrarily-viewed one. The main contribution of this paper is a frontalization methodology that preserves non-rigid facial deformations in order to boost the performance of visually assisted speech communication. The method alternates between the estimation of (i)~the rigid transformation (scale, rotation, and translation) and (ii)~the non-rigid deformation between an arbitrarily-viewed face and a face model. The method has two important merits: it can deal with non-Gaussian errors in the data and it incorporates a dynamical face deformation model. For that purpose, we use the generalized Student t-distribution in combination with a linear dynamic system in order to account for both rigid head motions and time-varying facial deformations caused by speech production. We propose to use the zero-mean normalized cross-correlation (ZNCC) score to evaluate the ability of the method to preserve facial expressions. The method is thoroughly evaluated and compared with several state of the art methods, either based on traditional geometric models or on deep learning. Moreover, we show that the method, when incorporated into deep learning pipelines, namely lip reading and speech enhancement, improves word recognition and speech intelligibilty scores by a considerable margin. Supplemental material is accessible at https://team.inria.fr/robotlearn/research/facefrontalization/