In this paper, novel second order and fourth order diffusion models are
proposed for image denoising. Both models are based on the gradient vector
convolution (GVC) model. The second model is coined by incorporating the GVC
model into the anisotropic diffusion model and the fourth order one is by
introducing the GVC to the You-Kaveh fourth order model. Since the GVC model
can be implemented in real time using the FFT and possesses high robustness
to noise, both proposed models have many advantages over traditional ones,
such as low computational cost, high numerical stability and remarkable
denoising effect. Moreover, the proposed fourth order model is an anisotropic
filter, so it can obviously improve the ability of edge and texture
preserving except for further improvement of denoising. Some experiments are
presented to demonstrate the effectiveness of the proposed models.