Regularization methods are a key tool in the solution of inverse problems. They are used to
introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses …

We describe a general strategy for the verification of variational source condition by
formulating two sufficient criteria describing the smoothness of the solution and the degree …

This paper is concerned with the classical inverse scattering problem to recover the
refractive index of a medium given near or far field measurements of scattered time …

The aim of this paper is to provide an overview of recent development related to Bregman
distances outside its native areas of optimization and statistics. We discuss approaches in …

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 …

We revisit in-spaces the autoconvolution equation with solutions which are real-valued or
complex-valued functions defined on a finite real interval, say. Such operator equations of …

In this chapter are outlined some aspects of the mathematical theory for direct regularization
methods aimed at the stable approximate solution of nonlinear illposed inverse problems …

We study the convergence of variationally regularized solutions to linear ill-posed operator
equations in Banach spaces as the noise in the right hand side tends to 0. The rate of this …

The book collects and contributes new results on the theory and practice of ill-posed inverse
problems. Different notions of ill-posedness in Banach spaces for linear and nonlinear …

We investigate a generalization of the well-known iteratively regularized Gauss–Newton
method where the Newton equations are regularized variationally using general data fidelity …