Local Analysis of Inverse Problems: Hölder Stability and Iterative Reconstruction

Maarten V. de Hoop, Lingyun Qiu, Otmar Scherzer

Published 2011-08-17, updated 2012-01-18Version 2

We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however, the data space can be an arbitrary Banach space. We study sequences of parameter functions generated by a nonlinear Landweber iteration and conditions under which these strongly converge, locally, to the solutions within an appropriate distance. We express the conditions for convergence in terms of H\"{o}lder stability of the inverse maps, which ties naturally to the analysis of inverse problems.