Inverse Scale Space Iterations for Non-Convex Variational Problems: The Continuous and Discrete Case

Nonlinear filtering approaches allow to obtain decomposition of images with respect to a non-classical notion of scale, induced by the choice of a convex, absolutely one-homogeneous regularizer. The associated inverse scale space flow can be obtained using the classical Bregman iteration with quadratic data term. We apply the Bregman iteration to lifted, i.e., higher-dimensional and convex, functionals in order to extend the scope of these approaches to functionals with arbitrary data term. We provide conditions for the subgradients of the regularizer – in the continuous and discrete setting– under which this lifted iteration reduces to the standard Bregman iteration. We show experimental results for the convex and non-convex case.