Spatial fractional telegraph equation for image structure preserving denoising

In this paper, we propose a spatial fractional telegraph equation which could be applied to image denoising. The proposed equation interpolates between the second and the fourth order anisotropic diffusion equation by the use of spatial fractional derivatives. On the other hand, the telegraph equation interpolates between diffusion equation and wave equation, which leads to a mixed behavior of diffusion and wave propagation and thus it can preserve edges in the highly oscillatory regions. The existence, uniqueness and stability of the solution of our model are proved in this paper. The experimental results indicate superiority of the proposed model over the existing methods. HighlightsFractional derivatives lead to a interpolation between second and fourth order models.Telegraph equation interpolates between a diffusion equation and a wave equation.Telegraph equation is beneficial to enhance edges.We have proved that the proposed model is well-posed.The stable and convergent numerical scheme is given.

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