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