  In this paper we present a new regularization term for variational image
restoration which can be regarded as a space-variant anisotropic extension of
the classical isotropic Total Variation (TV) regularizer. The proposed
regularizer comes from the statistical assumption that the gradients of the
target image distribute locally according to space-variant bivariate Laplacian
distributions. The highly flexible variational structure of the corresponding
regularizer encodes several free parameters which hold the potential for
faithfully modelling 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. A minimization algorithm
based on the Alternating Direction Method of Multipliers (ADMM) is presented
for the efficient numerical solution of the proposed variational model. Some
experimental results are reported which demonstrate the high-quality of
restorations achievable by the proposed model, in particular with respect to
classical Total Variation regularization.
