A weighted total variation model with a spatially varying regularization weight is considered.
Existence of a solution is shown, and the associated Fenchel predual problem is derived …

Based on the weighted total variation model and its analysis pursued in Hintermüller and
Rautenberg 2016, in this paper a continuous, ie, infinite dimensional, projected gradient …

The First Detailed Account of Statistical Analysis That Treats Models as Approximations The
idea of truth plays a role in both Bayesian and frequentist statistics. The Bayesian concept of …

In recent years, a great deal of effort has been expended on developing robust solutions for
images quality degradation caused mainly by noise. In this paper, we explore this area of …

In this paper we study the structure of solutions of the one dimensional weighted total
variation regularisation problem, motivated by its application in signal recovery tasks. We …

In this paper we are concerned with fully automatic and locally adaptive estimation of
functions in a “signal+ noise”-model where the regression function may additionally be …

The purpose of the present chapter is to bind together and extend some recent
developments regarding data-driven nonsmooth regularization techniques in image …

In this paper we present a spatially-adaptive method for image reconstruction that is based
on the concept of statistical multiresolution estimation as introduced in Frick et al.(Electron. J …

This paper is devoted to highly robust statistical methods with applications to image
analysis. The methods of the paper exploit the idea of implicit weighting, which is inspired by …

In this paper, we present a novel L 1-L 2-TV model for image deblurring that incorporates
spatially varying regularization parameters, addressing the challenge of mixed Gaussian …