STATE-SPACE REGULARIZATION - GEOMETRIC-THEORY

Regularization of nonlinear ill-posed inverse problems is analyzed for a class of problems that is characterized by mappings which are the c omposition of a well-posed nonlinear and an ill-posed linear mapping. Regularization is carried out in the range of the nonlinear mapping. I n applications this corresponds to the state-space variable of a parti al differential equation or to preconditioning of data. The geometric theory of projection onto quasi-convex sets is used to analyze the sta bilizing properties of this regularization technique and to describe i ts asymptotic behavior as the regularization parameter tends to zero.