A class of nonlocal tensor telegraph-diffusion equations applied to coherence enhancement

In this paper, we propose a nonlocal tensor telegraph-diffusion equation which could be applied to enhancement of coherent flow-like structures. The telegraph-diffusion equation interpolates between diffusion equation and wave equation, which lead to a mixed behaviour of diffusion and wave propagation and thus it can preserve edges in a highly oscillatory region. Replacing scalar-valued diffusivity function by diffusion tensor enables real anisotropic diffusion processes which may reveal advantages to enhance the flow-like structures. In addition, the nonlocal technique makes our model robust to noise. 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.