Abstract: Compressed sensing theory combines traditional sampling theory with compression theory, which has become a research hotspot in recent years. Based on the sparseness or compressibility of the image, the K-Means Singular Value Decomposition（K-SVD） algorithm is used to obtain the overcomplete dictionary, using the Gaussian random matrix as the measurement matrix and the regularized adaptive matching pursuit algorithm for compressed sensing reconstruction algorithm, the Regularization Adaptive Matching Pursuit algorithm based on K-SVD overcomplete dictionary（KSVD-RAMP） is proposed. It compares the objective evaluation indexes such as the Peak Signal to Noise Ratio（PSNR）, time and  relative error of the reconstructed image, and compares the proposed algorithm with the traditional greedy algorithm. Experimental results show that the proposed algorithm is 2~5 dB higher than the RAMP algorithm based on sparse representation of discrete wavelet. Therefore, the reconstructed image is improved in both visual effect and objective evaluation index.

Key words: compressed sensing, K-Means Singular Value Decomposition（K-SVD）, reconstruction algorithm, overcomplete dictionary

摘要： 压缩感知理论将采样理论与压缩理论合二为一，成为最近几年来的研究热点。主要依据图像的稀疏性或是可压缩性的特点，使用K-均值奇异值分解（K-Means Singular Value Decomposition，K-SVD）算法训练获得过完备字典，使用高斯随机矩阵作为测量矩阵，最后通过正则化自适应匹配追踪算法作为压缩感知重构算法，提出了K-SVD过完备字典的正则化自适应匹配追踪算法（KSVD Regularized Adaptive Matching Pursuit，KSVD-RAMP）。通过对重构图像的峰值信噪比、重构时间、相对误差等客观评价指标以及主观视觉上对所提算法以及传统的贪婪算法做对比。实验结果表明，该算法比基于离散小波稀疏表示的RAMP算法的峰值信噪比提升了2~6 dB。因此，该算法重构出的图像不管在视觉效果上，还是在客观评价指标上都有一定的改善。

关键词: 压缩感知, K-均值奇异值分解（K-SVD）, 重构算法, 过完备字典