Variational image restoration based on Poisson singular integral and curvelet-type decomposition space regularization

Image restoration is a core topic of image processing. In this paper, we consider a variational restoration model consisting of Poisson singular integral (PSI) and curvelet-type decomposition space seminorm as regularizer. The PSI is used to impose a priori constraint on appropriate Lipschitz spaces, wherein a wide class of nonsmooth images can be accommodated. The seminorm of curvelet-type decomposition space is equivalent to the weighted curvelet coefficients which optimal represent smooth and edge parts of image with spar-sity. We propose efficient algorithm to solve the optimization problem based on the Douglas-Rachford splitting (DRS) technique. Experimental results demonstrate that our proposed method can preserve important image features, such as edges and textures.