Abstract

The image denoising and segmentation is a fundamental task in many medical applications based on magnetic resonance image processing. This problem can be solved by means of nonlinear diffusive filters requiring the solution of evolutive partial differential equations. In this work a coupled system of linear and nonlinear diffusion-reaction equations is proposed and tested for denoising and segmentation of magnetic resonance images. The discretization of the coupled system by means of the Finite Element method is reported. The effectiveness of the model has been tested on MR images affected by gaussian, impulsive noise and also in the case of dynamic magnetic resonance images where the data are affected by noise in the frequency domain.