A fractional diffusion-wave equation with non-local regularization for image denoising

This paper introduces a novel fractional diffusion-wave equation with non-local regularization for noise removal. Using the fractional time derivative, the model interpolates between the heat diffusion equation and the wave equation, which leads to a mixed behavior of diffusion and wave propagation and thus it can preserve edges in a highly oscillatory region. On the other hand, the usual diffusion is used to reduce the noise whereas the non-local term which exhibits an anti-diffusion effect is used to enhance the image structure. We prove that the proposed model is well-posed, and the stable and convergent numerical scheme is also given in this paper. The experimental results indicate superiority of the proposed model over the baseline diffusion models. HighlightsThe fractional PDE interpolates between a diffusion equation and a wave equation.The anti-diffusion effect of the non-local term results in edge enhancement.We have proved that the proposed model is well-posed.The stable and convergent numerical scheme is given.We have discussed the choice of the parameters in our model.

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