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 sparsity. 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.