41 citations · 324 across the 37 of their papers we have counts for
7 papers · 1 filter
On fractional asymptotical regularization of linear ill-posed problems in Hilbert spaces
Ye Zhang, Bernd Hofmann
In this paper, we study a fractional-order variant of the asymptotical regularization method, called {\it Fractional Asymptotical Regularization (FAR)}, for solving linear ill-pose…
On the singular value decomposition of n-fold integration operators
Ronny Ramlau, Christoph Koutschan, Bernd Hofmann
In theory and practice of inverse problems, linear operator equations with compact linear forward operators having a non-closed range and mapping betwee…
Tikhonov regularization with l^0-term complementing a convex penalty: l^1 convergence under sparsity constraints
Wei Wang, Shuai Lu, Bernd Hofmann +1
Measuring the error by an l^1-norm, we analyze under sparsity assumptions an l^0-regularization approach, where the penalty in the Tikhonov functional is complemented by a general…
Tikhonov regularization in Hilbert scales under conditional stability assumptions
Herbert Egger, Bernd Hofmann
Conditional stability estimates allow us to characterize the degree of ill-posedness of many inverse problems, but without further assumptions they are not sufficient for the stabl…
Convergence rates of a penalized variational inequality method for nonlinear monotone ill-posed equations in Hilbert spaces
Robert Plato, Bernd Hofmann
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regu…
Penalty-based smoothness conditions in convex variational regularization
Bernd Hofmann, Stefan Kindermann, Peter Mathé
The authors study Tikhonov regularization of linear ill-posed problems with a general convex penalty defined on a Banach space. It is well known that the error analysis requires sm…