A. Alwehebi, H. Kim, and S. Kim (USA)
Magnetic resonance imaging (MRI), Gaussian distribution, Rician distribution, Partial differential equations (PDEs), Anisotropic diffusion, Equalized net diffusion
The magnitude data/imagery obtained from the magnetic resonance imaging (MRI) have been modeled by the Rician distribution. So has the noise in the imagery, although the noise has experimentally known nearly Gaussian. This article analyzes statistically that the noise in the magnitude MRI data is approximately Gaussian of mean zero and of the same variance as in the frequency-domain measurements. Based on the analysis, we introduce a novel partial differential equation (PDE)-based denoising model which can restore fine structures satisfactorily and simultaneously sharpen edges as needed. It has been numerically verified that the new model can reduce the noise satisfactorily, in 3-4 alternating direction iterations, with the residual (the difference between the original image and the restored image) being nearly edge-free. It has also been verified that the model can perform edge-enhancement effectively during the denoising of the magnitude MRI imagery. Numerical examples are provided to support the claim.
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