A Non-Local Structure Tensor Based Approach for Multicomponent Image Recovery Problems

Non-Local Total Variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the Structure Tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the non-local variations, jointly for the different components, through various $\ell_{1,p}$ matrix norms with $p \ge 1$. To facilitate the choice of the hyper-parameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented thanks to the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for multispectral and hyperspectral images. The results demonstrate the interest of introducing a non-local structure tensor regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods

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

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