一种高阶各向异性扩散小波收缩图像降噪算法

Image denoising algorithm based on high-order anisotropic-diffusion wavelet-shrinkage

图像可以看作是一个曲面,描述曲面上某点相对于球面的弯曲程度可以用高斯曲率。提出用高斯曲率来定义在图像上的能量泛函,并得到相应的欧拉方程,利用梯度下降法推出基于高斯曲率的高阶各向异性扩散方程。进而根据小波收缩与各向异性扩散等价性框架,提出一种高阶各向异性扩散小波收缩图像降噪算法。实验表明,此算法在去除噪声的同时能够很好地保持高频特征和边缘形状。

Image can be regarded as curved surface, and Gaussian Curvature can be used to describe the curve＇s degree of curved surface relative to ball. In this paper, Gaussian curvature was used to define the energy function on image, and then the Euler equation was obtained. Gaussian curvature-based high-order diffusion （GCBHD） was derived from the Euler equation by gradient decrease method. And then, based on the equivalence of wavelet shrinkage and anisotropic diffusion, a high-order anisotropic-diffusion wavelet-shrinkage image denoising algorithm （GCBHDWS） was proposed. The experimental results show that GCBHDWS can maintain the high frequency and the shape of edge while denoising image.