D. Gerth

activity

20132022

most citedA new interpretation of (Tikhonov) regularization

34 citations · 62 across the 12 of their papers we have counts for

collaborators

Showing 2017 · math.FAShow all

2 papers · 2 filters

math.FA2017

On $ℓ^{1}$ -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 $ℓ^{1}$ -regularization as a sparsity-enforcing version of Tikhonov regula…

math.FA2017★ 1 cited

Injectivity and weak*-to-weak continuity suffice for convergence rates in $ℓ^{1}$ -regularization

Jens Flemming, Daniel Gerth

We show that the convergence rate of $ℓ^{1}$ -regularization for linear ill-posed equations is always $O (δ)$ if the exact solution is sparse and if the considered operator is injec…

On ℓ1-regularization under continuity of the forward operator in weaker topologies

Injectivity and weak*-to-weak continuity suffice for convergence rates in ℓ1-regularization

On $ℓ^{1}$ -regularization under continuity of the forward operator in weaker topologies

Injectivity and weak*-to-weak continuity suffice for convergence rates in $ℓ^{1}$ -regularization