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 …

We consider a bilevel optimisation approach for parameter learning in higher-order total
variation image reconstruction models. Apart from the least squares cost functional, naturally …

We review some recent learning approaches in variational imaging based on bilevel
optimization and emphasize the importance of their treatment in function space. The paper …

We propose a new variational framework to remove a mixture of Gaussian and impulse
noise from images. This framework is based on a non-convex PDE-constrained with a …

In the present work, we investigate the inverse problem of identifying simultaneously the
denoised image and the weighting parameter that controls the balance between two …

Design and optimal control problems are among the fundamental, ubiquitous tasks we face
in science and engineering. In both cases, we aim to represent and optimize an unknown …

We introduce a method for the fast estimation of data-adapted, spatially and temporally
dependent regularization parameter-maps for variational image reconstruction, focusing on …

We propose a bilevel optimization approach for the estimation of parameters in nonlocal
image denoising models. The parameters we consider are both the fidelity weight and …

This chapter provides an overview of current developments in the fast growing field of
machine learning for medical image reconstruction. A comprehensive overview of recent …

We consider the problem of image denoising in the presence of noise whose statistical
properties are a combination of two different distributions. We focus on noise distributions …