Heuristic parameter selection based on functional minimization: Optimality and model function approach

We analyze some parameter choice strategies in regularization of inverse problems, in particular, the (modified) L-curve method and a variant of the Hanke–Raus type rule. These are heuristic rules, free of the noise level, and they are based on minimization of some functional. We analyze these functionals, and we prove some optimality results under general smoothness conditions. We also devise some numerical approach for finding the minimizers, which uses model functions. Numerical experiments indicate that this is an efficient numerical procedure