Data Based Regularization Matrices for the Tikhonov-Phillips Regularization

In Tikhonov-Phillips regularization of general form the given ill-posed linear system is replaced by a Least Squares problem including a minimization of the solution vector x, relative to a seminorm with some regularization matrix L. Based on the finite difference matrix L_k, given by a discretization of the first or second derivative, we introduce the seminorm where the diagonal matrix and is the best available approximate solution to x. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)