On regularization methods based on dynamic programming techniques

Abstract

In this article, we investigate the connection between regularization theory for inverse problems and dynamic programming theory. This is done by developing two new regularization methods, based on dynamic programming techniques. The aim of these methods is to obtain stable approximations to the solution of linear inverse ill-posed problems. We follow two different approaches and derive a continuous and a discrete regularization method. Regularization properties for both methods are proved as well as rates of convergence. A numerical benchmark problem concerning integral operators with convolution kernels is used to illustrate the theoretical results.

Keywords:

• Inverse problems
• Regularization
• Dynamic programming

Keywords:

• AMS Classifications: 65J22
• 49N45

Acknowledgments

The work of S.K. is supported by Austrian Science Foundation under grant SFB F013/F1317; the work of A.L. is supported by the Austrian Academy of Sciences and by CNPq, grant 306020/06-8 and 478099/04-5.