基于TL1范数的改进K-SVD字典学习算法

摘要

K-SVD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,用OMP(Orthogonal Matching Pursuit)算法求解稀疏表示,用SVD分解算法对字典更新.但应用在图像重构时,OMP算法运行速度比较慢,且恢复的准确度不够高.针对该问题,为了提高字典训练速度与性能,在稀疏编码阶段用TL1范数代替了l0范数,用迭代阈值算法求解稀疏表示.为考察改进算法的恢复准确率,在不同稀疏度下进行数据合成实验,结果表明改进算法比K-SVD算法训练恢复的准确率高.进一步考察改进算法的图像重构能力,选取标准图像进行仿真,实验结果表明改进算法比K-SVD算法能更快得到训练字典,获得更高的峰值信噪比(PSNR),具有更好的重构性能.%K-SVD dictionary learning algorithm is employed to obtain the training dictionary by using sparse coding and dic?tionary updating iteratively,in which Orthogonal Matching Pursuit algorithm(OMP)is used to get the sparse expressions in the sparse coding stage,while the SVD algorithm is utilized to update the dictionary.However,when it is applied into the image recon?struction,the Orthogonal Matching Pursuit algorithm(OMP)is slower and its accuracy is not satisfied.Aiming at this problem,To improve the speed and performance of training dictionary,l0is replaced with TL1in the sparse coding stage,and the iterative thresh?old algorithm is used to the sparse expressions.To test the performance of the proposed algorithm,date synthesis experiment is con?ducted under different sparse degree,and these results show that the proposed algorithm is better than the K-SVD.To further test the performance of the proposed algorithm,the standard image is used to simulate and the experimental results show that the pro?posed algorithm is faster than K-SVD to obtain the training dictionary,and has higher PSNR and better reconstruction performance.