Recovering a function or high-dimensional parameter vector from indirect measurements is
a central task in various scientific areas. Several methods for solving such inverse problems …

Regularization methods aimed at finding stable approximate solutions are a necessary tool
to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of …

Conventional light microscopes have been used for centuries for the study of small length
scales down to approximately 250 nm. Images from such a microscope are typically blurred …

Motivated by the theoretical and practical results in compressed sensing, efforts have been
undertaken by the inverse problems community to derive analogous results, for instance …

This paper investigates the theoretical guarantees of ℓ^1-analysis regularization when
solving linear inverse problems. Most of previous works in the literature have mainly focused …

A variational model for image reconstruction is introduced and analyzed in function space.
Specific to the model is the data fidelity, which is realized via a basis transformation with …

We generalize the notion of Bregman distance using concepts from abstract convexity in
order to derive convergence rates for Tikhonov regularization with non-convex …

We present a general framework to study uniqueness, stability and reconstruction for infinite-
dimensional inverse problems when only a finite-dimensional approximation of the …

The goal of this paper is the formulation of an abstract setting that can be used for the
derivation of linear convergence rates for a large class of sparsity promoting regularization …

Variational source conditions proved to be useful for deriving convergence rates for
Tikhonov's regularization method and also for other methods. Up to now, such conditions …