Multiscale methods for polyhedral regularizations (Q2866192)

The inverse scale space flow is a continuous formulation of the augmented Lagrangian method. The paper reviews the adaptive inverse scale space (aISS) method for polyhedral functions. The authors generalize the aISS method to any convex polyhedral functions in fg-representation. The convergence properties of the method are analyzed and the finite time convergence is proved. The forward inverse scale space flow is shown to be the inverse scale space flow on the convex conjugate problem and can be solved by the aISS algorithm. A certain case of forward scale space flows is shown to be equivalent to a known variational problem. Some numerical examples are provided to show that the aISS method is applicable for a variety of regularized or constrained problems if the fg-representation is sufficiently low-dimensional and if the true solution is sparse in its ic-representation.