Iterated Adaptive Regularization for the Operator Equations of the First Kind

Summary

The adaptive regularization method is first proposed by Ryzhikov et a1 in [RB98] for the deconvolution in elimination of multiples which appears in geoscience and remote sensing. They have done experiments to show this method is very effective. This method is stronger than the Tikhonov regularization in the sense that it is adaptive, i.e., it automatically eliminates the small singular values of the operator when which is nearly singular. In this paper, we will show that the adaptive regularization can be implemented in an iterated way. Particularly, we show that if some priori knowledge-based information (i.e., a priori strategy for choosing the regularization parameter) is known in advance, the order of the convergence rate can approach O(δ4ν/4ν+1) for some ν > 0. A posteriori strategy for choosing the regularization parameter is also introduced, the regularity is proved.

Jointly Sponsored by the Institute of Remote Sensing Applications of Chinese Academy of Sciences and Beijing Normal University

The work is partly supported by Chinese national 973 research project G20000779.