二维小波收缩与各向异性扩散等价性框架及在图像去噪中的应用

图像去噪是图像处理中的一种重要技术。小波收缩根据噪声的小波系数幅值较小的特征通过收缩达到去噪目的。各向异性扩散在尽可能保持图像特征的同时，根据梯度方向及幅值去噪。该文首先证明二维小波收缩与各向异性扩散的等价性框架，对等价性给予验证，进而根据等价性提出综合利用两种方法优势的各向异性小波收缩去噪算法。对比实验结果表明，此算法综合利用了小波收缩与各向异性扩散的优势，去噪效果更加理想。

The Equivalence Framework and the Application to Image Denoising of Two Dimensional Wavelet Shrinkage and Anisotropic Diffusivity

Image denoising is one of important technology in image processing. The denoising image can be gotten by shrink the amplitude of wavelet coefficient of noise according to the fact that it is smaller than others in Wavelet Shrinkage (WS). The Anisotropic Diffusivity (AD) completes denoising according to the direction and amplitude of gradient while as far as possible to keep the characteristic of image. In this paper, the equivalence framework of two dimensional wavelet shrinkage and anisotropic diffusivity is proved with experiment. After that, the Anisotropic Wavelet Shrinkage (AWS) is proposed that synthesizes the merits of the wavelet shrinkage and anisotropic diffusivity according to the equivalence. The contrastive experiments show that the AWS is better for image denoising.