在应用扩散方程进行图像平滑时，常规的方法是对扩散方程差分化构造差分方程，利用初边值条件求解。这种方法误差传播快，精度不高。因此，构造了2维小波插值函数，利用它来求解扩散方程，并分析得到用小波插值函数求解Alvarez模型的方法。由于小波函数具有良好的局部性，求解扩散方程比用差分方法求解具有精度高，误差传播速度慢，对时间步长不敏感等优点。在数值实验中，给出了本文方法的有效性及相对于差分方法求解的优点。

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.