Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 44-57 |
| Journal | ISAST Transactions on Electronics and Signal Processing |
| Volume | 4 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2010 |
| Externally published | Yes |
Keywords
- anisotropic diffusion
- noise reduction
- digital images
- non-Gaussian
- Levy distributed
- fractional diffusion equation
- Levy index
- numerical algorithm
- magnetic resonance imaging
- diffusion weighted images
- low signal-to-noise ratios
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