Abstract: K-Singular Value Decomposition （K-SVD） algorithm is often used for image denoising by creating an over-complete dictionary for sparse representation. K-SVD algorithm is effective and can keep the original image information as well. However, the image structure is often ignored. Furthermore, noise atoms are still existed in the trained dictionary obtained by K-SVD algorithm, which will result?in the poor denoising performance. According to these limitations, a new denoising algorithm is proposed in this paper. First, a more targeted dictionary is obtained by the classification of noisy image blocks. Second, the dictionary atoms are classified into the noise and noiselesscategories, and then the optimized dictionary will be achieved by replacing the noise atoms by overcomplete?discrete cosine transform dictionary atoms. Third, the image is denoised using the optimized dictionary. Simulation studies show that in comparison with the curvelet-based denoising method, the non-local mean denoising method and the classical K-SVD denoising method, the new approach has better denoising ability.

Key words: image denoising, sparse representation, K-Singular Value Decomposition （K-SVD） algorithm, image blocks classification, overcomplete dictionary, dictionary optimization

摘要： 基于K-奇异值分解（K-SVD）的图像去噪方法使用K-SVD算法训练得到的过完备字典对图像进行稀疏表示去噪，能够在去除噪声的同时较好地保持原始图像信息。但该方法缺少对图像结构特征的考虑；此外，K-SVD算法训练得到的字典中往往含有噪声原子，从而导致该方法在强噪声下去噪性能欠佳。针对这些局限性，提出一种新的去噪方法：基于块分类和字典优化的K-SVD去噪方法。首先通过图像块的分类训练得到与图像结构相适应的字典，能够更为稀疏地表示图像；然后通过噪声原子检测将字典原子分为噪声原子和非噪声原子，并对噪声原子进行替换，减弱噪声原子对去噪性能的影响，得到优化字典；利用优化字典对图像进行稀疏表示去噪。仿真实验表明，与非局部均值去噪、曲波去噪以及经典K-SVD去噪等算法相比，新方法能够取得更好的去噪结果。

关键词: 图像去噪, 稀疏表示, K-SVD算法, 图像块分类, 过完备字典, 字典优化