A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection
This work provides a more flexible and automated regularisation method for image restoration, benefiting researchers and practitioners in image processing who need to preserve fine details and textures.
The paper introduces a space-variant anisotropic regularisation term for image restoration, derived from a bivariate generalised Gaussian distribution model of local image gradients. It achieves significant quality improvement over state-of-the-art methods, particularly in texture and detail preservation, with automated parameter selection via robust maximum likelihood estimation.
We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian distribution. The highly flexible variational structure of the corresponding regulariser 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. For the numerical solution of the corresponding image restoration model, we use an iterative algorithm based on the Alternating Direction Method of Multipliers (ADMM). A suitable preliminary variable splitting together with a novel result in multivariate non-convex proximal calculus yield a very efficient minimisation 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.