63 citations · 200 across the 10 of their papers we have counts for
6 papers · 1 filter
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…
Empirical Risk Minimization as Parameter Choice Rule for General Linear Regularization Methods
Housen Li, Frank Werner
We consider the statistical inverse problem to recover from noisy measurements where is Gaussian white noise and a compact operator between Hilbert spaces…
Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise
Claudia König, Frank Werner, Thorsten Hohage
This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain…
Convergence Rates for Inverse Problems with Impulsive Noise
Thorsten Hohage, Frank Werner
We study inverse problems F(f) = g with perturbed right hand side g^{obs} corrupted by so-called impulsive noise, i.e. noise which is concentrated on a small subset of the domain o…
Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data
Frank Werner, Thorsten Hohage
In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations $\gdag = F(\udag)$ where $\gdag$ is an integrable, non-negative function. We assume that da…
Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
Thorsten Hohage, Frank Werner
We study Newton type methods for inverse problems described by nonlinear operator equations in Banach spaces where the Newton equations ar…