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

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VMV - Variational methods and effective algorithms for imaging and vision

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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