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1.2 COMPUTER AND INFORMATION SCIENCE
We extend the method of anisotropic diffusion for noise reduction in digital images to the case when the diffusion processes are non-Gaussian and Levy distributed. This yields a fractional diffusion equation characterised by the Levy 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.
Blackledge, J., Blackledge, M.: Fractional Anisotropic Diffusion for Noise Reduction in Magnetic Resonance Images. ISAST Transactions on Electronics and Signal Processing, vol 4, issue 1, pp. 44 - 57. 2010. doi:10.21427/D7491X