An improved model function method for choosing regularization parameters in linear inverse problems

摘要

This paper proposes a new model function iterative method, that improves our earlier work (Kunisch K and Zou J 1998 Inverse Problems 14 1247-64), on finding some reasonable regularization parameters in the widely used output least squares formulations of linear inverse problems, based on the Morozov and damped Morozov principles. The new algorithm updates the model parameters in a computationally more stable manner. In addition, he method can be rigorously shown to have global convergence, in particular, its convergence is carried on strictly monotone decreasingly. This property seems especially useful and important in real applications as it enables us to start with some larger regularization parameters, and thus with more stable least squares problems. Numerical experiments for one- and two-dimensional elliptic inverse problems and an inverse integral problem are presented to illustrate the efficiency of the proposed algorithm.