小波域上图像非线性扩散滤波

提出一个小波域上图像扩散滤波恢复新模型。主要思想是把原图像作为最精细尺度下的小波子带，根据噪声分布的特点，导出保护较大尺度下信息的泛函模型代替小波阈值除噪，对泛函求变分得：Euler-Lagrange方程。新的滤波方法能避免小波阈值除噪的伪Gibbs现象，改进了同类型非线性扩散方程滤波的效果。利用可加算子分裂(AOS)格式求非线性扩散方程的数值解。实例的数值计算说明对图像滤波和保护边缘的有效性。

Anisotropic Diffusion Filtering for Image Restoration on Wavelet Domain

In image processing, removal of noise without blurring the image edges is a difficult problem. Typically, noise is characterized by high spatial frequencies in image. A new method for image denoising is proposed on wavelet domain, based on image multiresolution decomposition and anisotropic diffusion filtering. The original image can be regarded as high resolution wavelet sub-sampling one. A functional of preserved lower resolution information is presented. It is used to substitute for wavelet threshold denoising on image. The Euler-Lagrange equations are deduced from the variational principle by the image functional model. Image is denoised and enhanced simultaneously. The numerical schemes of the equation is based on additive operator splitting (AOS) scheme. Some experimental results demonstrate the validity of the new method for image denoising and edge preserving. And this method is also compared with other denoising methods, such as wavelets threshold filtering and anisotropic diffusion filtering. The numerical results of the application on images demonstrate the good performance of the new method.