41 citations · 324 across the 37 of their papers we have counts for
5 papers · 1 filter
Convergence results and low order rates for nonlinear Tikhonov regularization with oversmoothing penalty term
Bernd Hofmann, Robert Plato
For the Tikhonov regularization of ill-posed nonlinear operator equations, convergence is studied in a Hilbert scale setting. We include the case of oversmoothing penalty terms, wh…
Case studies and a pitfall for nonlinear variational regularization under conditional stability
Daniel Gerth, Bernd Hofmann, Christopher Hofmann
Conditional stability estimates are a popular tool for the regularization of ill-posed problems. A drawback in particular under nonlinear operators is that additional regularizatio…
Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates
Frank Werner, Bernd Hofmann
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this…
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…
A new class of accelerated regularization methods, with application to bioluminescence tomography
Rongfang Gong, B. Hofmann, Ye Zhang
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is…