Finite-dimensional approximation of convex regularization via hexagonal pixel grids

Abstract

This work extends the existing convergence analysis for discrete approximations of minimizers of convex regularization functionals. In particular, some solution concepts are generalized, namely the standard minimum norm solutions for squared-norm regularizers and the -minimizing solutions for general convex regularizers, respectively. A central part of the manuscript addresses finite-dimensional approximations of solutions of ill-posed operator equations with basis functions defined on hexagonal grids, which require the novel solution concept.