Convergence analysis is carried out for a forward-backward splitting/generalized gradient
projection method for the minimization of a special class of non-smooth and genuinely non …

The stable solution of ill-posed non-linear operator equations in Banach space requires
regularization. One important approach is based on Tikhonov regularization, in which case a …

A computational Bayesian inversion model is demonstrated. It is discretization invariant,
describes prior information using function spaces with a wavelet basis and promotes …

The multiscale hierarchical decomposition method (MHDM) was introduced in Tadmor et al
(2004 Multiscale Model. Simul. 2 554–79; 2008 Commun. Math. Sci. 6 281–307) as an …

Variational sparsity regularization based on ℓ 1-norms and other nonlinear functionals has
gained enormous attention recently, both with respect to its applications and its …

We consider regularization of nonlinear ill-posed problems with constraints which are non-
convex. As a special case, we consider separable constraints, ie the regularization takes …

We consider region of interest (ROI) tomography of piecewise constant functions.
Additionally, an algorithm is developed for ROI tomography of piecewise constant functions …

We study the regularising properties of Tikhonov regularisation on the sequence space ℓ2
with weighted, non-quadratic penalty term acting separately on the coefficients of a given …

Although the residual method, or constrained regularization, is frequently used in
applications, a detailed study of its properties is still missing. This sharply contrasts the …

Using a sparsity promoting penalty term in the Tikhonov regularization scheme has been
shown to be efficient in reconstructing solutions which own a sparse structure. These penalty …