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On the existence of weak solutions of the Perona-Malik equation

Presented by: 
Kewei Zhang
Tuesday 26th September 2017 - 15:00 to 16:00
INI Seminar Room 1
The Perona-Malik forward-backward diffusion model is a well-known device in image processing to reduce noise and enhance edges. However due to its forward-backward nature, the Perona-Malik model is mathematically ill-posed. I will describe a differential inclusion method to solve the one-dimensional version of the Perona-Malik equation under the homogeneous Neumann boundary condition. Possible constructions of staircase solutions are also suggested.  Recent development on higher dimensional cases are also briefly described.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons