In image smoothing with diffusion equation

general methods are to construct difference equation of diffusion

then solve it with initialization and edge condition. These methods have low precision and diffuse error quickly. So a wavelet interpolation method is structured in this paper and is applied to solve the diffusion equation. We get a method to Alvarez model by two-dimensional wavelet interpolation method. Wavelet function possess better partial character

compared with finite difference method

wavelet method has higher precision

slower speed of error diffusion

and not is sensitive to time interval. The experiment shows the advantages of this method compared with difference method.