41 citations · 324 across the 37 of their papers we have counts for
5 papers · 1 filter
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…
Oversmoothing Tikhonov regularization in Banach spaces
De-Han Chen, Bernd Hofmann, Irwin Yousept
This paper develops a Tikhonov regularization theory for nonlinear ill-posed operator equations in Banach spaces. As the main challenge, we consider the so-called oversmoothing sta…
On -regularization under continuity of the forward operator in weaker topologies
Daniel Gerth, Bernd Hofmann
Our focus is on the stable approximate solution of linear operator equations based on noisy data by using -regularization as a sparsity-enforcing version of Tikhonov regula…
Elastic-net regularization versus -regularization for linear inverse problems with quasi-sparse solutions
De-Han Chen, Bernd Hofmann, Jun Zou
We consider the ill-posed operator equation with an injective and bounded linear operator mapping between and a Hilbert space , possessing the unique solutio…
On -regularization in light of Nashed's ill-posedness concept
Jens Flemming, Bernd Hofmann, Ivan Veselic
Based on the powerful tool of variational inequalities, in recent papers convergence rates results on -regularization for ill-posed inverse problems have been formulated in…