Directional total generalized variation regularization

Directional Total Generalized Variation Regularization for Impulse Noise Removal

Regularization of linear inverse problems with total generalized variation

The regularization properties of the total generalized variation (TGV) functional for the solution of linear inverse problems by means of Tikhonov regularization are studied. Considering the associated minimization problem for general symmetric tensor fields, the wellposedness is established in the space of symmetric tensor fields of bounded deformation, a generalization of the space of functio...

Total Variation Regularization in

We propose computational algorithms for incorporating total varia-tional (TV) regularization in positron emission tomography (PET). The motivation for using TV is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of PET where the objective is to identify the shape of objects...

Total Generalized Variation

The novel concept of total generalized variation of a function u is introduced and some of its essential properties are proved. Differently from the bounded variation semi-norm, the new concept involves higher order derivatives of u. Numerical examples illustrate the high quality of this functional as a regularization term for mathematical imaging problems. In particular this functional selecti...

Discrete Total Variation Flows without Regularization

We propose and analyze an algorithm for the solution of the L2-subgradient flow of the total variation functional. The algorithm involves no regularization, thus the numerical solution preserves the main features that motivate practitioners to consider this type of energy. We propose an iterative scheme for the solution of the arising problems, show that the iterations converge, and develop a s...