We discuss a model for quadratic variational denoising that approximates smoothness terms of arbitrary order by a coupling of the solution and auxiliary variables such that a system of partial differential equations of second order is obtained. We show that the model maintains a continuous as well as discrete integrability property between coupling variables. In the discrete setting an algorithm is presented that yields the desired solution analytically and refrains from calculating any auxiliary variables.

This presentation is part of Minisymposium “MS5 - Learning and adaptive approaches in image processing (2 parts)”
organized by: Kostas Papafitsoros (Weierstrass Institute Berlin) , Michael Hintermüller (Humboldt University and Weierstrass Institute Berlin) .

Authors:

Aaron Wewior (Saarland University)

Keywords:

image reconstruction, numerical linear algebra, partial differential equation models