41 citations · 67 across the 9 of their papers we have counts for
9 papers
The degree of ill-posedness of composite linear ill-posed problems with focus on the impact of the non-compact Hausdorff moment operator
Bernd Hofmann, Peter Mathé
We consider compact composite linear operators in Hilbert space, where the composition is given by some compact operator followed by some non-compact one possessing a non-closed ra…
Designing truncated priors for direct and inverse Bayesian problems
Sergios Agapiou, Peter Mathé
The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study…
Nonlinear Tikhonov regularization in Hilbert scales with oversmoothing penalty: inspecting balancing principles
Bernd Hofmann, Christopher Hofmann, Peter Mathé +1
The analysis of Tikhonov regularization for nonlinear ill-posed equations with smoothness promoting penalties is an important topic in inverse problem theory. With focus on Hilbert…
Inverse learning in Hilbert scales
Abhishake Rastogi, Peter Mathé
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regula…
Lepskii Principle in Supervised Learning
Gilles Blanchard, Peter Mathé, Nicole Mücke
In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regulari…
A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems
Bernd Hofmann, Peter Mathé
We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to hav…
Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales
Bernd Hofmann, Peter Mathé
We study the Tikhonov regularization for ill-posed non-linear operator equations in Hilbert scales. Our focus is on the interplay between the smoothness-promoting properties of the…
Preconditioning the prior to overcome saturation in Bayesian inverse problems
Sergios Agapiou, Peter Mathé
We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the s…
A new perspective on the Propagation-Separation approach: Taking advantage of the propagation condition
Saskia Becker, Peter Mathé
The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean…