Abstract: The basic idea of compressed sensing theory is that the original signal is sparse in a transform domain or compressible, and the sampling process and the compression process in the Nyquist sampling theorem are combined into one. Sparse Adaptive Matching Pursuit（SAMP） algorithm can realize the reconstruction under unknown sparsity, and the generalized orthogonal matching pursuit algorithm selects multiple atoms at each iteration, which improves the convergence speed of the algorithm. This paper proposes a Generalized Sparse Adaptive Matching Pursuit（gSAMP） algorithm based on the advantages of the above two reconstruction algorithms, and then the peak signal to noise ratio, reconstruction time, relative error, etc. of the reconstructed image are proposed. Objective evaluation indicators and subjective visual comparisons of the proposed algorithm and the traditional greedy algorithm. When the compression ratio is fixed at 0.5, the reconstruction effect of the gSAMP algorithm is better than that of the traditional greedy reconstruction algorithms such as MP, OMP, ROMP, SAMP and gOMP.

Key words: compressed sensing, Sparsity Adaptive Matching Pursuit（SAMP）, sparsity, generalized orthogonal matching pursuit, greedy reconstruction algorithm

摘要： 压缩感知理论的基本思想是原始信号在某一变换域是稀疏的或者是可压缩的，并将奈奎斯特采样定理中的采样过程和压缩过程合二为一。稀疏度自适应匹配追踪（SAMP）算法能够实现稀疏度未知情况下的重构，而广义正交匹配追踪算法每次迭代时选择多个原子，提高了算法的收敛速度。基于上述两种重构算法的优势，提出了广义稀疏度自适应匹配追踪（Generalized Sparse Adaptive Matching Pursuit，gSAMP）算法。针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与传统的贪婪算法进行对比。在压缩比固定为0.5时，gSAMP算法的重构效果优于传统的MP、OMP、ROMP、SAMP以及gOMP贪婪类重构算法的效果。

关键词: 压缩感知, 稀疏度自适应匹配追踪, 稀疏度, 广义正交匹配追踪, 贪婪类重构算法