The investigation of regularization schemes with sparsity promoting penalty terms has been
one of the dominant topics in the field of inverse problems over the last years, and Tikhonov …

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 …

The subject of inverse problems in differential equations is of enormous practical
importance, and has also generated substantial mathematical and computational …

Inverse problems arise in practical applications whenever one needs to deduce unknowns
from observables. This monograph is a valuable contribution to the highly topical field of …

In this paper we establish a mathematical framework for a range of inverse problems for
functions, given a finite set of noisy observations. The problems are hence underdetermined …

For O a bounded domain in Rd and a given smooth function g: O→ R, we consider the
statistical nonlinear inverse problem of recovering the conductivity f> 0 in the divergence …

In this paper we discuss the construction, analysis and implementation of iterative schemes
for the solution of inverse problems based on total variation regularization. Via different …

We consider a class of inverse problems defined by a nonlinear map** from parameter or
model functions to the data, where the inverse map** is Hölder continuous with respect to …

Ill-posed problems are encountered in countless areas of real world science and
technology. A variety of processes in science and engineering is commonly modeled by …

In this paper, we propose and analyze a two-point gradient method for solving inverse
problems in Banach spaces which is based on the Landweber iteration and an extrapolation …