Smooth objectives composed of asymptotically affine data-fidelity and regularization. Bounds for the minimizers and parameter choice
Résumé
We examine properties of the minimizer u* of a class of differentiable functionals where both the data-term and the regularization term are symmetric and nearly affine beyond a small neighborhood of the origin. Customarily, such functions are used to regularize a quadratic data-fidelity term in order to produce solutions where edges are preserved. The functionals we consider in this paper behave quite differently. They were recently successfully applied to provide a strict order for the pixels of digital (quantized) images f thus enabling exact histogram specification. We give upper and lower bounds for the error $\|u* - f\|_\infty$, where the upper bound is independent of the input image f. Interestingly, in the numerical experiments with natural digital images f, the estimated upper bound is easily reached up to a small error. To explain this phenomenon we give simple statistical estimates for the behavior of neighboring pixels. We apply our estimates to specify the parameters of the model.
Domaines
Analyse numérique [math.NA]
Origine : Fichiers produits par l'(les) auteur(s)