Regularization of ill-posed problems by using stabilizers in the form of the total variation of a function and its derivatives

Abstract

AbstractUnder the assumption that the solution of a linear operator equation is presented in the form of a sum of several components with various smoothness properties, a modified Tikhonov regularization method is studied. The stabilizer of this method is the sum of three functionals, where each one corresponds to only one component. Each such functional is either the total variation of a function or the total variation of its derivative. For every component, the convergence of approximate solutions in a corresponding normed space is proved and a general discrete approximation scheme for the regularizing algorithm is justified.