In this paper we present the extension and generalization of the adaptive inverse scale space (aISS) method proposed for l1 regularization in [BMBO11] to arbitrary polyhedral functions. We will see that the representation of a convex polyhedral function as a nitely generated function yields a fast and general aISS algorithm. We analyze its convergence and interpret the well known (forward) scale space flow as the inverse scale space flow on the convex conjugate functional, thus including this class of flows in our analysis. A surprising result is the equivalence of the scale space or gradient flow with a standard variational problem. Finally, we give some examples of the applications for the adaptive inverse scale space algorithm for polyhedral functions.

@TechReport{MB11,
  author       = {Moeller, M. and Burger, M.},
  title        = {Multiscale Methods for polyhedral regularizations},
  institution  = {UCLA},
  number       = {11-74},
  year         = {2011},
  type         = {CAM Report},
  url          = \{/2011/MB11},
}