A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection

We propose a new space-variant anisotropic regular ization term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalized Gaussian distribution. The highly flexible variational structure of the corresponding regularizer encodes several free parameters which hold the potential for faithfully modeling the local geometry in the image and describing local orientation preferences. For an automatic estimation of such parameters, we design a robust maximum likelihood approach and report results on its reliability on synthetic data and natural images. For the numerical solution of the corresponding image restoration model, we use an iterative algorithm based on the alternating direction method of multipliers. A suitable preliminary variable splitting together with a novel result in multivariate nonconvex proximal calculus yield a very efficient minimization algorithm. Several numerical results showing significant quality improvement of the proposed model with respect to some related state-of-the-art competitors are reported, in particular, in terms of texture and detail preservation.