TY - UNPB

T1 - Inverse Scale Space Iterations for Non-Convex Variational Problems

T2 - The Continuous and Discrete Case

AU - Bednarski, Danielle

AU - Lellmann, Jan

N1 - 15 pages, 6 figures, submitted for JMIV special issue. arXiv admin note: substantial text overlap with arXiv:2105.02622

PY - 2022/3/21

Y1 - 2022/3/21

N2 - 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.

AB - 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.

M3 - Preprint

BT - Inverse Scale Space Iterations for Non-Convex Variational Problems

ER -