基于Shearlet域各向异性扩散和稀疏表示的图像去噪

为了更有效地去除图像噪声，同时更好地保留图像边缘细节信息，提出了一种基于shearlet 域各向异性扩散和稀疏表示的图像去噪方法. 首先对含噪图像进行非下采样shearlet 变换(nonsubsampled shearlet transform, NSST)，将图像分解为低频分量和多个高频分量. 低频分量中包含图像信号的主要能量以及少量的噪
声，而高频分量中含有大部分噪声和图像边缘信息. 然后，利用K-奇异值分解(K-singular value decomposition,K-SVD) 算法去除低频分量中的噪声，各个方向的高频分量则通过核各向异性扩散(kernel anisotropic diffusion,KAD) 算法进行去噪. 最后，对处理过的低频分量和高频分量进行非下采样shearlet 反变换(inverse nonsubsampled shearlet transform, INSST)，得到重构图像，从而有效地去除图像噪声，保留图像边缘细节. 实验结果表明，与小波扩散去噪法、shearlet 硬阈值去噪法、K-SVD 稀疏去噪法、小波域稀疏去噪法相比，该方法的去噪能力更强，并能更好地保留图像纹理细节特征，改善图像视觉效果.

Image Denoising Based on Anisotropic Diffusion and Sparse Representation in Shearlet Domain

To suppress image noise effectively and better preserve edge details, an image denoising method
based on anisotropic diffusion and sparse representation in the shearlet domain is proposed. The noisy image is
first decomposed into a low frequency component and several high frequency components by non-subsampled
shearlet transform (NSST). The main energy of the image information is contained in the low frequency
component, while the edge information and most of noise are contained in high frequency components. The K-singular value decomposition (K-SVD) algorithm is used to remove noise in low frequency component. The kernel anisotropic diffusion (KAD) algorithm is used to reduce noise in each high frequency component. The reconstructed image is obtained by inverse non-subsampled shearlet transform (INSST) for the processed low frequency and high frequency components. Noise in the image is effectively suppressed, and edge details are preserved satisfactorily. Experimental results show that, compared with the denoising methods such as wavelet combining with nonlinear diffusion method, shearlet hard threshold method, K-SVD sparse denoising method and sparse redundant denoising method in wavelet domain, the proposed method has better performance both in noise reduction and detail preservation.