基于双树复小波与波原子的图像扩散滤波

图像的非线性扩散滤波来源于热方程的思想,其关键在于计算适当的扩散系数和控制扩散方向. 在已有的扩散模型中,由于扩散系数仅依赖于图像的梯度,因而这类模型容易受噪声的干扰;同时,图像的细节信息(如纹理)容易被误认为是噪声而被去除. 为克服这些不足,首先给出了一种采用双树复小波变换计算扩散系数的方法;然后设计了一种用于图像滤波的非线性扩散模型,最后提出了基于双树复小波变换和波原子阈值相结合的图像滤波算法. 仿真结果表明,所提出的算法在对含噪图像滤波的同时,能够较好地保持图像的边缘和纹理等细节信息.关键词：图像扩散滤波非线性扩散波原子双树复小波变换

Image diffusion filtering based on dual tree complex wavelet and wave atoms

The nonlinear diffusion of image filtering is from the idea of heat equations. Its key point is to choose a proper diffusion coefficient and control the diffusion direction. In the previous models, the diffusivity depends on the gradients of images, thus it is easily affected by noises. Furthermore, many fine structures such as textures are prone to being taken for noise and then will be removed. In order to overcome these shortcomings, first, in this paper we introduce a novel computational technique for diffusivity by using the dual tree complex wavelet transform. Second, we develop a nonlinear diffusion model for image filtering. Finally, an image diffusion filtering method based on the dual tree complex wavelet transform and wave atoms thresholding is presented, and also compared with the previous methods. Experimental results show that many features of image such as edges and textures can be preserved well after filtering via the proposed algorithm.