Inverse scale space theory for inverse problems

Abstract

In this paper we derive scale space methods for inverse problems which satisfy the fundamental axioms of fidelity and causality and we provide numerical illustrations of the use of such methods in deblurring. These scale space methods are asymptotic formulations of the Tikhonov-Morozov regularization method. The analysis and illustrations relate diffusion filtering methods in image processing to Tikhonov regularization methods in inverse theory. © Springer-Verlag Berlin Heidelberg and IEEE/CS 2001.