Giovanni S Alberti,Matteo Santacesaria,Silvia Sciutto Giovanni S Alberti

In this work, we present and study Continuous Generative Neural Networks (CGNNs), namely, generative models in the continuous setting: the output of a CGNN belongs to an infinite-dimensional function space. The architecture is inspired by D...

Mehrsa Pourya,Sebastian Neumayer,Michael Unser Mehrsa Pourya

We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze theore...

Peter Balazs,Helmut Harbrecht Peter Balazs

For the solution of operator equations, Stevenson introduced a definition of frames, where a Hilbert space and its dual are not identified. This means that the Riesz isomorphism is not used as an identification, which, for example, does not...

Clemens Kirisits,Otmar Scherzer Clemens Kirisits

In the context of convex variational regularization, it is a known result that, under suitable differentiability assumptions, source conditions in the form of variational inequalities imply range conditions, while the converse implication o...

V Albani,P Elbau,M V de Hoop et al. V Albani et al.

In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general so...