Study On Magnetic Resonance Image Denoising Based On Partial Difference Equations

Magnetic resonance imaging(MRI) has been applied widely in the medical diagnosis and the scientific research for its unique characters such as non-invasive, imaging mechanism with several parameters and the capacity of reflecting in vivo organization, energy metabolism features etc. However, the noise caused by imaging mechanism, the outside environment as well as the patients etc maybe corrupt MR image so that it is hard for doctors to discover the abnormity. Therefore, it is very important to improve the quality of MR image by post-processing.Image denoising based on PDE has received increased attention recently. Perona and Malik proposed a PDE model based on anisotropic diffusion in 1990. Since that day many scholars have improved the P-M model. Alvarez, Lions and Morel introduced the Mean Curvature Motion equation in 1992. The model can preserve the diffusion only in the orthogonal direction of gradient and remove noise from an image while preserving the edge.The basic principle of denoising methods for MR image: there is no artifact in post-processing image; the original abnormity can not disappear after the post-processing; the filter process can not bring new abnormity. MCM and AMSS are both classical PDE models. However, there is few report on the MR image denoising effect of the two PDE models.This thesis is focused on two aspects. Firstly, according to the theory of PDE image denoising, we analyze noise characteristic in MR image, algorithm for discretization of MCM and AMSS models and the denoising effect of the two PDE models. The experimental results show that MCM and AMSS models can both remove noise of MR images effectively.Secondly, we compare the denoising effect of the two PDE models and wavelet transform. A new strategy for denoising MR image is proposed. The new strategy combines the wavelet denoising and the anisotropic diffusion. The experimental results show that the new filter strategy can achieve very similar denoising effect as ContextVison's software.