Inverse scale spaces for nonlinear regularization
Error minimization of global functionals provides a natural setting for analyzing image processing and regularization. This approach leads to scale spaces, which in the continuous formulation are the solution of nonlinear partial differential equations. In this work we derive properties for a class of inverse scale space methods. The main contribution of this paper is the development of a proof that the methods considered are convergent for convex regularization operators. The proof is based on energy methods and the Bregman distance. Further, estimates for convergence toward a clean image with noisy forcing data is provided in terms of both the L (2) norm and Bregman distances. This leads to natural estimates of optimal stopping scale for the inverse scale space method. These analytical results are discussed in the context of a numerical example.
inverse scale space bregman distance pde image denoising energy minimization