The total variation (TV) minimization models are widely used in image processing, 16 mainly due to their remarkable ability in preserving edges. There are many methods 17 for solving the TV model. These methods, however, seldom consider the positivity con18 straint one should impose on image-processing problems. In this paper we develop and 19 implement a new approach for TV image restoration. ...

In the Rudin-Osher-Fatemi (ROF) image denoising model, Total Variation (TV) is used as a global regularization term. However, as we observe, the local interactions induced by Total Variation do not propagate much at long distances in practice, so that the ROF model is not far from being a local filter. In this paper, we propose to build a purely local filter by considering the ROF model in a gi...

We study the extension of total variation (TV), total deformation (TD), and (second-order) total generalised variation (TGV) to symmetric tensor fields. We show that for a suitable choice of finite-dimensional norm, these variational semi-norms are rotation-invariant in a sense natural and well-suited for application to diffusion tensor imaging (DTI). Combined with a positive definiteness const...

Fig. 3: TGV2 Image reconstruction of undersampled radial data with 48, 32 and 24 spokes. Conventional NUFFT reconstruction (left), TV (middle) and TGV2 (right). Fig. 4: Magnified views from Fig. 3. Conventional NUFFT reconstruction (left), TV (middle) and TGV2 (right). Fig. 1: Illustration of TV (middle) and TGV2 (right) denoising of a numerical ramp image. Total Generalized Variation (TGV) for...

Total Variation (TV) regularization is a popular method for solving a wide variety of inverse problems in image processing. In order to optimize the reconstructed image, it is important to choose a good regularization parameter. The Unbiased Predictive Risk Estimator (UPRE) has been shown to give a good estimate of this parameter for Tikhonov regularization. In this paper we propose an extensio...

This paper presents an evaluation of the use of Primal Dual Methods for efficiently regularizing the electric impedance tomography (EIT) problem with the Total Variation (TV) functional. The Total Variation functional is assuming an important role in the regularization of inverse problems thanks to its ability to preserve discontinuities in reconstructed profiles. This property is desirable in ...

In this paper, a novel weighted nonlocal total variation (WNTV) method is proposed. Compared to the classical nonlocal total variation methods, our method modifies the energy functional to introduce a weight to balance between the labeled sets and unlabeled sets. With extensive numerical examples in semi-supervised clustering, image inpaiting and image colorization, we demonstrate that WNTV pro...

Quasi-stationary distributions, as discussed in Darroch and Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present...

In this paper we study the decay of solutions to parabolic conservation laws in the Hardy space H 1 and in the total variation norm. We show that solutions to scalar equations and systems decay to zero without a rate in H 1 , and that the total variation of solutions decays to zero at an algebraic rate.