Inverse Scale Space Iterations for Non-Convex Variational Problems Using Functional Lifting

Abstract

Non-linear filtering approaches allow to obtain decompositions of images with respect to a non-classical notion of scale. The associated inverse scale space flow can be obtained using the classical Bregman iteration applied to a convex, absolutely one-homogeneous regularizer. In order to extend these approaches to general energies with non-convex data term, we apply the Bregman iteration to a lifted version of the functional with sublabel-accurate discretization. We provide a condition for the subgradients of the regularizer under which this lifted iteration reduces to the standard Bregman iteration. We show experimental results for the convex and non-convex case.

13 pages, 3 figures, accepted at the conference "Scale Space and Variational Methods" 2021