Regularization for surface representations of discontinuous solutions of linear ill-posed problems

In this paper we deal with a regularization method for ill-posed problems well-suited for solutions with discontinuities, regularization for surface representations. It is a generalization of the recently developed method regularization for curve representations, which has been successfully applied to linear and nonlinear one-dimensional ill-posed problems, to two-dimensional problems. We prove convergence of the finite-dimensional Tikhonov regularized solutions and present some numerical results.