Finite difference and Legendre spectral method for a time-fractional diffusion-convection equation for image restoration
Moulay Rchid Sidi Ammi Ismail Jamiai
Discrete & Continuous Dynamical Systems - S 2018, 11(1): 103-117 doi: 10.3934/dcdss.2018007

In this paper, we consider a time fractional diffusion-convection equation and its application for image processing. A time discretization scheme is introduced and a stability result and error estimates are proved. Practical experiments are then provided showing that the fractional approach is more efficient than the ordinary integer one (Perona-Malik). A fully discrete scheme is proposed by using a Legendre collocation method. The convergence of this method is obtained by proving a priori error estimates.

keywords: Fractional calculus image processing noise reduction image enhancement finite difference method Legendre spectral method

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