Space-Adaptive Anisotropic Bivariate Laplacian Regularization for Image Restoration

In this paper we present a new regularization term for variational image restoration which can be regarded as a space-variant anistropic extension of the classical Total Variation (TV) regularizer. The proposed regularizer comes from the statistical assumption that the gradients of the unknown target image distribute locally according to space-variant bivariate Laplacian distributions. The high flexibility of the proposed regularizer holds the potential for the effective modelling of local image properties, in particular driving in an adaptive manner the strength and the directionality of non-linear TV-diffusion. The free parameters of the regularizer are automatically set - and, eventually, updated - based on a robust Maximumum Likelihood estimation procedure. A minimization algorithm based on the Alternating Direction Method of Multipliers is presented for the efficient numerical solution of the proposed variational model. Some experimental results are reported. They demonstrate the high-quality of restorations achievable by the proposed model, in particular with respect to classical TV-regularized models.