Fractional Anisotropic Diffusion for Noise Reduction in Magnetic Resonance Images

We extend the method of anisotropic diffusion for noise reduction in digital images to the case when the diffusion processes are non-Gaussian and Lévy distributed. This yields a fractional diffusion equation characterised by the Lévy index. A solution to this equation is considered and a numerical algorithm developed. The algorithm is then applied as a case study to the problem of reducing noise in magnetic resonance imaging. The focus of this study is on diffusion weighted images which have low signal-to-noise ratios.

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