Generalized reaction–diffusion equations

This Letter proposes generalized reaction–diffusion equations for treating noisy magnetic resonance images. An edge-enhancing functional is introduced for image enhancement. A number of super-diffusion operators are introduced for fast and effective smoothing. Statistical information is utilized for robust edge-stopping and diffusion-rate estimation. A quasi-interpolating wavelet algorithm is utilized for numerical computations. Computer experiments indicate that the present algorithm is efficient for edge detecting and noise removing. The generalized reaction–diffusion equations have potential applications in modeling boundary-restricted diffusion, multiphase chemical reactions and reaction–diffusion in porous media.