The Poisson Factor Analysis (PFA) is applied to recover signals from a Poisson compressive sensing system. Motivated by the recently developed compressive X-ray imaging system, Coded Aperture Coherent Scatter Spectral Imaging (CACSSI) [1], we propose a new Bayesian reconstruction algorithm. The proposed Poisson-Gamma (PG) approach uses multiple measurements to refine our knowledge on both sensing matrix and background noise to overcome the uncertainties and inaccuracy of the hardware system. Therefore, a collaborative compressive X-ray image reconstruction algorithm is proposed under a Bayesian framework. Experimental results on real data show competitive performance in comparison with point estimation based methods.