Nonlinear diffusion is a well-established tool for image denoising and enhancement. Whereas traditionally, nonnegative diffusivities are considered, it has been observed since long that backward diffusion plays a pivotal role for e.g. edge enhancement, provoking interest in diffusivities that even admit negative values. Then, the inherent instability of backward diffusion must be controlled. We discuss recent approaches to this problem, including nonstandard spatial discretisations, adaptive time-stepping schemes and special boundary conditions.

This presentation is part of Minisymposium “MS15 - Nonlinear Diffusion: Models, Extensions and Algorithms (2 parts)”
organized by: Ke Chen (University of Liverpool) , Joachim Weickert (Saarland University) , Xue-Cheng Tai (Hong Kong Baptist University) .

Authors:

Martin Welk (Private University for Health Sciences, Medical Informatics and Technology (UMIT))

Keywords:

adaptive numerical schemes, dynamical systems, image enhancement, partial differential equation models