Automated measurement of the intensity of spontaneous facial Action Units (AU) defined by the Facial Action Coding System (FACS) in video sequences is a challenging problem. This paper proposes a person-adaptive methodology for the intensity estimation of spontaneous AUs. We formulate this problem as a source separation problem where we consider the observed AUs as the source signals to be separated from each other and other information given by a sequence of facial images. We first compute an initial estimation of the sources, called observations, using sparse linear regression functions. We then develop and apply a Bayesian source separation method that recruits the prior information of the sources to iteratively improve the initial estimations/observations in an adaptive fashion. Furthermore, our approach adaptively uses some testing information (but not the ground-truth labels) to improve the performance of the approach (i.e., Person-Adaptive model). Our experimental results on DISFA, UNBC-McMaster and FERA2015 databases show that this approach is very promising for automated measurement of the intensity of spontaneous facial AUs.