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Colour Image Denoising: Numerical Approximation of the Constrained Total Variation Flow

Vera Jackisch

Dienstag, 26. Januar 2021 14:15Uhr

The Rudin-Osher-Fatemi model is a well-known denoising model for greyscale images. One approach to adapt this model to colour images involves computing the total variation flow constrained to a manifold. In a recent work by Giga et al., an algorithm to approximate the constrained total variation flow is proposed and a discretisation using piecewise constant functions is presented. As piecewise constant functions are generally not suited to approximate functions of bounded variation, we present a similar algorithm using piecewise affine finite elements, in particular Crouzeix-Raviart elements. We show stability of the scheme, experimental convergence rates and some improved denoising results. This work is the result of my master thesis.