DK8: Nonlinear regularization methods for the solution of linear ill-posed problems

Regularization methods for linear ill-posed problems Kf = g have been extensively investigated when there exists noisy measurements gδ for the true data g. However, often also the operator is not known exactly. A common way to solve this problem is to use the regularized total least squares method.

The goal of this project is to extend this theory towards the infinite dimensional setting for nonlinear operators. Recently we proposed a new approach to solve bilinear operators. In particular, we are interested in providing a complete analysis: regularization properties, parameter choice and convergence rates. Moreover, we aim to develop an efficient algorithm in order to solve problems with real data.

Supervisor: Prof. Ronny Ramlau