王少慧， 曹艳华^*

（  华北电力大学数理学院信息与计算研究所，北京　102206；  ）

摘要： 压缩感知理论是近几年提出的一种全新的信号采样理论。针对压缩感知中未知稀疏度信号的重建问题，提出一种改进的回溯自适应匹配追踪算法。该算法将压缩采样匹配追踪算法中的回溯思想，分段正交匹配追踪算法中的自适应思想相结合，在信号稀疏度未知的情况下，自适应地在每次迭代中选择支撑集原子的个数，然后利用回溯思想，同时引入参数,从已选中的原子中，再次选择出较大投影系数所对应的原子，实现支撑集的二次筛选，最终实现信号的精确重构。仿真结果表明，该算法能够精确的重构原始信号，从恢复误差上进行对比，重建效果优于正交匹配追踪（Orthogonal Matching Pursuit, OMP）算法，广义正交匹配追踪(Generalized OMP, gOMP)算法，稀疏度自适应匹配追踪（Sparsity adaptive matching pursuit，SAMP）算法，分段弱正交匹配追踪(Stagewise Weak OMP,SWOMP) 算法。
关键词： 压缩感知；回溯；自适应；匹配追踪；重构

WANG Shaohui， CAO Yanhua^*

（  Institute of Information and Computation, Mathematics and Physics Department, North China Electric Power University, Beijing 102206；  ）

Abstract： Compressed sensing theory is a new signal sampling theory proposed in recent years. Facing the problem of reconstruct signals with unknown sparsity in compressed sensing, this paper presents an improved backtracking adaptive matching pursuit algorithm. The proposed algorithm combines the idea of backtracking in the compressed sampling matching pursuit algorithm and the idea of adaptive in piecewise orthogonal matching pursuit algorithm, the number of support set atoms can be selected adaptively in each iteration with unknown sparsity of signals. And then it uses the idea of backtracking, the atoms corresponding to the projection coefficients which are bigger are selected again from the selected atoms through introducing parameter ,so that realizes the second selecting of the atoms in the support set. Finally, the new algorithm can achieve the accuracy of reconstruction. The simulation results show that the proposed algorithm can reconstruct the original signal accurately, and it outperforms Orthogonal Matching Pursuit(OMP) algorithm, Generalized OMP(gOMP) algorithm, Sparsity Adaptive Matching Pursuit (SAMP) algorithm, and Stagewise Weak OMP(SWOMP) algorithm from comparing their reconstruction error.
Keywords： compressed sensing; backtracking; adaptive; matching pursuit; reconstruction

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