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Stable Models and Algorithms for Backward Diffusion Evolutions

By Joachim Weickert

Appears in collection : Variational methods and optimization in imaging

Backward diffusion equations are potentially useful for image enhancement and deblurring. However, these processes are regarded as typical representatives for ill-posed problems that suffer from intrinsic instabilities. These difficulties have prevented many researchers from using such evolutions. The goal of this talk is to show that this fear is unsubstantiated, provided that one supplements the models with suitable stabilisation techniques and takes care that the numerical algorithms reproduce all qualitative properties of the continuous models in an adequate way. Prototypical models include forward-backward diffusion processes and repulsive particle systems with range constraints. Joint work with Martin Welk (UMIT), Leif Bergerhoff (Saarland University), Marcelo Càrdenas (Saarland University), and Guy Gilboa (Technion).

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