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

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