基于非线性小波阈值的各向异性扩散方程

An Anisotropic Diffusion Equation Based on Nonlinear Wavelet Shrinkage

本文给出了林石算子定义的扩散方程的小波阈值等价形式,并在此基础上对林石算子定义的扩散系数计算公式进行了修改,将其中估计各阶导数时所用的高斯线性滤波图像改成平移不变小波非线性阈值图像,这样避免了高斯滤波引起的过度光滑和边界移动.实验结果表明新的扩散方程在保持边缘位置的同时能更有效地去除噪声.

This paper presents an equivalent formation via wavelet threshold of the diffusion equation defined by Lin-shi operator. Based on the equivalent formation, there are some revisions made for the diffusion coefficient by replacing the Gaussian filtered image with the translational-invariant nonlinear wavelet thresholded image when do estimation of all the derivation levels. This revision will be able to avoid the over-smoothness and edge movement resulting from the Ganssian filter. Finally, experimental results show that the new diffusion equation is effective to eliminate noise while maintaining the edge locations.