  Non-linear filtering approaches allow to obtain decompositions 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.
