Combining Poisson singular integral and total variation prior models in image restoration

In this paper, a novel Bayesian image restoration method based on a combination of priors is presented. It is well known that the Total Variation (TV) image prior preserves edge structures while imposing smoothness on the solutions. However, it tends to oversmooth textured areas. To alleviate this problem we propose to combine the TV and the Poisson Singular Integral (PSI) models, which, as we will show, preserves the image textures. The PSI prior depends on a parameter that controls the shape of the filter. A study on the behavior of the filter as a function of this parameter is presented. Our restoration model utilizes a bound for the TV image model based on the majorization-minimization principle, and performs maximum a posteriori Bayesian inference. In order to assess the performance of the proposed approach, in the experimental section we compare it with other restoration methods.