中文摘要：

提出了一种ALM-KSVD字典学习算法,通过稀疏编码和字典更新两步迭代学习得到训练样本的字典.为了提高字典训练速度与性能,在稀疏编码引入增广拉格朗日乘子法（ALM,Augmented Lagrange Multipliers）求解,更新字典则使用经典K-SVD的字典更新算法.为考察算法的字典训练速度和平均表示误差（RMSE）,选取了不同样本数和噪声标准进行数据合成实验,结果表明本文算法比经典的K-SVD算法字典训练速度快、RMSE低.进一步考察算法的图像去噪能力,选取不同的输入图像噪声标准和字典原子数进行仿真,实验结果表明本文算法比经典的K-SVD算法获得更高的峰值信噪比（PSNR）,具有良好的去噪性能.

英文摘要：

An improvement of K-SVD dictionary learning algorithm has been proposed, through the two-stage iteration of sparse coding and dictionary update. In order to improve the dictionary training speed and performance, Augmented Lagrangian multiplier method（ALM） is introduced in the sparse coding stage, while the standard K-SVD dictionary updating algorithm is used in the dictionary updating stage. In this work, the dictionary training speed and root-mean-square error（RMSE） of the algorithm are investigated in the synthesis date experiment by selecting different sample sets and noise standards. The results show that the algorithm is better than the standard K-SVD dictionary learning, which receives faster training speed and lower RMSE. In order to investigate the image denoising ability of the algorithm, simulation experiment is carried out by selecting different input image noise standards and the atomic numbers of the dictionary. The algorithm shows higher peak signal-to-noise ratio（PSNR） and better denoising performance than the standard K-SVD algorithm.