A family of rules for the choice of the regularization parameter in the Lavrentiev method in the case of rough estimate of the noise level of the data

作者：Haemarik Uno; Palm Reimo; Raus Toomas

来源：Journal of Inverse and Ill-Posed Problems, 2012, 20(5-6): 831-854.

DOI：10.1515/jip-2012-0061

• Ill-posed problems
• noise level
• regularization
• Lavrentiev method
• regularization parameter choice

We consider the Lavrentiev method for the regularization of linear ill-posed problems with noisy data. Classical rules for the choice of the regularization parameter that use the noise level work well for almost exact noise level information, they fail in the case of the underestimated noise level and give a much larger error than the error by the optimal parameter in the case of the overestimated noise level. Heuristic rules that do not use the noise level give often good results but can not guarantee the convergence. We propose a general family of parameter choice rules, which give good results also in the case of many times under-or overestimated noise level. This family combines heuristic rules and quasi-optimal rules that use the noise level. The quasi-optimality is proved for a sub-family of rules. The advantages of the new rules are demonstrated in extensive numerical experiments.

• 出版日期2012-12