Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms

摘要

We consider the nonstationary iterated Tikhonov regularization in Banachspaces which defines the iterates via minimization problems with uniformlyconvex penalty term. The penalty term is allowed to be non-smooth to include$L^1$ and total variation (TV) like penalty functionals, which are significantin reconstructing special features of solutions such as sparsity anddiscontinuities in practical applications. We present the detailed convergenceanalysis and obtain the regularization property when the method is terminatedby the discrepancy principle. In particular we establish the strong convergenceand the convergence in Bregman distance which sharply contrast with the knownresults that only provide weak convergence for a subsequence of the iterativesolutions. Some numerical experiments on linear integral equations of firstkind and parameter identification in differential equations are reported.