In this paper, a new restoration method for the X-ray images with optical blurs and quantum mottles is proposed by considering the physical formation process of X-ray images. More specifically, the optical blurs are first deterministically cleared away by using the transfer characteristic of the laser scanning, the characteristic of the radiographic screen-film system, the logarithmic transformation of the optical density and a digital inverse filter based on the point spread function. Next, as a restoration method for remaining quantum mottles, a wide sense digital filter of a stochastic type using the statistical properties of quantum mottles is newly derived on the basis of a Bayes' theorem matched to the recursive image processing. Finally, in order to confirm the effectiveness of the proposed method, it is applied to one of the actual medical images.