A REGULARIZATION PARAMETER FOR NONSMOOTH TIKHONOV REGULARIZATION

In this paper we develop a novel rule for choosing regularization parameters in non-smooth Tikhonov functionals. It is solely based on the value function and applicable to a broad range of nonsmooth models, and it extends one known criterion. A posteriori error estimates of the approximations are derived. An efficient numerical algorithm for computing the minimizer is developed, and its convergence properties are discussed. Numerical results for several common nonsmooth models are presented, including deblurring natural images. The numerical results indicate the rule can yield results comparable with those achieved with the discrepancy principle and the optimal choice, and the algorithm merits a fast and steady convergence.