Image-modeling Gibbs distributions for Bayesian restoration

Gibbs distributions have been widely used in the Bayesian approach to many image processing problems. However, little attention has been paid to whether or not the Gibbs distribution indeed models the images that occur in the particular area of application. Indeed, random samples from many of the proposed Gibbs distributions are likely to be uniformly smooth, and thus atypical for any application area. The authors investigate the possibility of finding Gibbs distributions which truly model certain global properties of images. Specifically, they construct a Gibbs distribution which models an image that consist of piecewise homogeneous regions by including different orders of neighbor interactions. By sampling the Gibbs distribution which arises from the model, they obtain images with piecewise homogeneous regions resembling the global features of the image that they intend to model; hence such a Gibbs distribution is indeed “image-modeling”. They assess the adequacy of their model using a χ² goodness-of-fit test. They also address how parameters are selected based on given image data. Importantly, the most essential parameter of the image model (related to the regularization parameter) is estimated in the process of constructing the image model. Comparative results are presented of the outcome of using their model and an alternative model as the prior in some image restoration problems in which noisy synthetic images were considered