Regularization methods are a key tool in the solution of inverse problems. They are used to
introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses …

Over the last decades, the total variation (TV) has evolved to be one of the most broadly-
used regularisation functionals for inverse problems, in particular for imaging applications …

We introduce a family of adaptive estimators on graphs, based on penalizing the l 1 norm of
discrete graph differences. This generalizes the idea of trend filtering (Kim et al., 2009; …

In this paper we study a variational problem in the space of functions of bounded Hessian.
Our model constitutes a straightforward higher-order extension of the well known ROF …

We present nonquadratic Hessian-based regularization methods that can be effectively
used for image restoration problems in a variational framework. Motivated by the great …

We introduce a novel family of invariant, convex, and non-quadratic functionals that we
employ to derive regularized solutions of ill-posed linear inverse imaging problems. The …

Total variation denoising is a nonlinear filtering method well suited for the estimation of
piecewise-constant signals observed in additive white Gaussian noise. The method is …

This review discusses methods for learning parameters for image reconstruction problems
using bilevel formulations. Image reconstruction typically involves optimizing a cost function …

We introduce a novel generic energy functional that we employ to solve inverse imaging
problems within a variational framework. The proposed regularization family, termed as …

Total variation methods and similar approaches based on regularizations with ℓ 1-type
norms (and seminorms) have become a very popular tool in image processing and inverse …