Before revision:  The existence of such a discrete scheme was proved by Yarvin and Rokhlin, 16 . Our algorithm models the regularization constant C for the linear part of the inverse problem as a random variable allowing us to sweep through a wide range of possible values. We show in simulations that this is crucial when the noise level is not known .
After revision:  The existence of such a discrete scheme was proved by Yarvin and Rokhlin, 16 Simply put, our proof only assumes that the regularized discrete error functional for processing measurements relates to an order 1 quadrature rule and that the union of the finite-dimensional spaces for discretizing slips is dense. Our proof relies on trace class operator theory to show that an adequate sequence of determinants is uniformly bounded .