基于稀疏表示与非局部相似的图像去噪算法

Image denoising algorithm based on sparse representation and nonlocal similarity

针对受加性高斯白噪声(AWGN)与椒盐噪声(SPIN)以及随机值冲击噪声(RVIN)组成的混合噪声污染的图像进行去噪的问题,提出一种在现有加权编码算法的基础上将图像稀疏表示和非局部相似先验融合的改进算法。首先,利用基于字典的图像稀疏表示构建去噪变分模型,对模型中的数据保真项设计一个权重因子来抑制冲击噪声的干扰;其次,利用非局部平均思想对混合噪声图像进行初始去噪,在得到的图像中构建掩膜矩阵将冲击噪声点排除进而求取非局部相似先验知识;最后,将非局部相似先验与稀疏先验融合进变分模型的正则项中,求解变分模型得到最终去噪图像。实验结果表明,在不同的噪声比率下,所提算法与模糊加权非局部平均算法相比,峰值信噪比(PSNR)提高了1.7 d B,特征相似性指数(FSIM)提高了0.06;与加权编码算法相比,PSNR提高了0.64 d B,FSIM提高了0.03。该算法对于纹理较强的图像可以显著提升去噪效果,能有效地保留图像的本真信息。

For the problem of denoising images corrupted by mixed noise such as Additive White Gaussian Noise（ AWGN） with Salt-and-Pepper Impulse Noise（ SPIN） and Random-Valued Impulse Noise（ RVIN）, an improved image restoration algorithm on the basis of the existing weighted encoding method was proposed. The image priors about sparse representation and non-local similarity were integrated. Firstly, the sparse representation based on the dictionary was used to build a variational denoising model and a weighting factor was designed for data fidelity term to suppress impulse noise.Secondly, the method of non-local means was used to get an initialized denoised image and then a mask matrix was built to remove impulse noise points to get the good non-local similarity prior knowledge. Finally, the image sparsity prior and nonlocal similarity prior were integrated into the regularization of the variational model. The final denoised image was obtained by solving the variational model. The experimental results show that in different noise ratios, the Peak Signal-to-Noise Ratio（ PSNR） of the proposed algorithm increased 1. 7 d B than that of fuzzy weighted non-local means filter, and the Feature Similarity Index（ FSIM） increased 0. 06. Compared with weighted encoding method, the PSNR increased 0. 64 d B, and the FSIM increased 0. 03. The proposed method has better recovery performance especially for the texture strong images and can retain real information of the image.