Estimation of linear functionals from indirect noisy data without knowledge of the noise level

Abstract

In this paper we discuss how one can avoid the use of information about levels of data noise and operator perturbations in the regularization of ill-posed linear operator equations. We present an approach that allows an estimation of linear functionals on the solutions with the best possible order of the accuracy uniformly over classes of solutions and admissible functionals. Proposed approach is based on the concept of distance functions and employs a deterministic version of the balancing principle. We argue that this approach can be of interest in satellite geodesy.