Directional convergence of spectral regularization method associated to families of closed operators

MAZZIERI, GISELA L; SPIES, RUBÉN D; TEMPERINI, KARINA G

COMPUTATIONAL AND APPLIED MATHEMATICS

Springer

Año: 2013 vol. 32 p. 119 - 134

We consider regularized solutions of linear inverse ill-posed problems obtained withgeneralized Tikhonov-Phillips functionals with penalizers given by linear combinationsof seminorms induced by closed operators. Convergence of the regularized solutions isproved when the vector regularization rule approaches the origin through appropriateradial and diferentiable paths. Characterizations of the limiting solutions are given.Finally, a examples of image restoration using generalized Tikhonov-Phillips methodswith convex combinations of seminorms are shown.