Authors: Janev, Marko 
Pilipović, Stevan
Atanacković, Teodor
Obradović, Radovan
Ralević, Nebojša
Title: Fully fractional anisotropic diffusion for image denoising
Journal: Mathematical and Computer Modelling
Volume: 54
Issue: 1-2
First page: 729
Last page: 741
Issue Date: 1-Jul-2011
Rank: M21
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2011.03.017
This paper introduces a novel Fully Fractional Anisotropic Diffusion Equation for noise removal which contains spatial as well as time fractional derivatives. It is a generalization of a method proposed by Cuesta which interpolates between the heat and the wave equation by the use of time fractional derivatives, and the method proposed by Bai and Feng, which interpolates between the second and the fourth order anisotropic diffusion equation by the use of spatial fractional derivatives. This equation has the benefits of both of these methods. For the construction of a numerical scheme, the proposed partial differential equation (PDE) has been treated as a spatially discretized Fractional Ordinary Differential Equation (FODE) model, and then the Fractional Linear Multistep Method (FLMM) combined with the discrete Fourier transform (DFT) is used. We prove that the analytical solution to the proposed FODE has certain regularity properties which are sufficient to apply a convergent and stable fractional numerical procedure. Experimental results confirm that our model manages to preserve edges, especially highly oscillatory regions, more efficiently than the baseline parabolic diffusion models.
Keywords: Anisotropic diffusion | Fractional derivatives | Fractional linear multistep methods | Fractional order differences | Fractional ordinary differential equations | Image denoising
Publisher: Elsevier
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
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Methods of Functional and Harmonic Analysis and PDE with Singularities 
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