A sure-fired way to choose smoothing parameters in ill-conditioned inverse problems

摘要

Regularisation methods for the solution of inverse problems are well known although the theoretical study of their performance especially in image processing contexts is not well advanced. What is also much less resolved is smoothing or penalty parameter estimation. We describe a general procedure for estimation of auxiliary finite dimensional parameters in ill-conditioned inverse problems. The method is applicable to nonlinear problems, involves no approximations but offers computational advantages over cross validation and maximum likelihood.