Bayesian Image Processing

ABSTRACT Many image processing problems can be presented as inverse problems by modeling the relation of the observed image to the unknown desired features explicitly. Some of these problems are naturally presented as inverse problems such as restoration of blurred images (deconvolution) or image reconstruction in computed tomography. For some others, we need to translate the original problem as an inverse one. For example, image de-noising, image segmentation or even image compression can also be presented as inverse problems. The main advantage of doing so is that we can then use probabilistic modeling of the images and use the Bayesian estimation approach to propose new methods for them. In this paper, we present a very general forward modeling for the observations and a very general probabilistic modeling of images through a hidden Markov modeling (HMM) which can be used as the main basis for many image processing problems such as: 1) simple or multi channel image restoration, 2) simple or joint image segmentation, 3) multi-sensor data and image fusion and 4) Principal Component Analysis (PCA), Factor Analysis (FA), Independent Component Analysis (ICA) and blind source separation.