41 citations · 324 across the 37 of their papers we have counts for
40 papers
New results for variational regularization with oversmoothing penalty term in Banach spaces
Bernd Hofmann, Chantal Klinkhammer, Robert Plato
In this article on variational regularization for ill-posed nonlinear problems, we are once again discussing the consequences of an oversmoothing penalty term. This means in our mo…
Newton's methods for solving linear inverse problems with neural network coders
Otmar Scherzer, Bernd Hofmann, Zuhair Nashed
Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear in…
A note on the degree of ill-posedness for mixed differentiation on the d-dimensional unit cube
Bernd Hofmann, Hans-Jürgen Fischer, Robert Plato
Numerical differentiation of a function, contaminated with noise, over the unit interval by inverting the simple integration operator $J:L^2([0,1]) \to L…
On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case
Bernd Hofmann, Frank Werner, Yu Deng
This paper analyzes the inverse problem of deautoconvolution in the multi-dimensional case with respect to solution uniqueness and ill-posedness. Deautoconvolution means here the r…
Deautoconvolution in the two-dimensional case
Yu Deng, Bernd Hofmann, Frank Werner
There is extensive mathematical literature on the inverse problem of deautoconvolution for a function with support in the unit interval , but little is kno…
Variational regularization with oversmoothing penalty term in Banach spaces
Robert Plato, Bernd Hofmann
In the present work, we discuss variational regularization for ill-posed nonlinear problems with focus on an oversmoothing penalty term. This means in our model that the searched-f…