Abstract: Facing the problem of reconstruct signals with unknown sparsity in compressed sensing, this paper presents a new signal reconstruction algorithm, named Adaptive Regularized Subspace Pursuit（ARSP） algorithm. The proposed algorithm is associated with adaptive process and regularized process and Subspace Pursuit algorithm（SP）. The new algorithm can achieve the accuracy of reconstruction by choosing the support set adaptively, and exploiting the regularization process which realizes the second selecting of the atoms in the support set although the sparsity of the original signal is unknown. The simulation results show that the proposed algorithm can reconstruct the original signal accurately, and it outperforms SP algorithm, Regularized Orthogonal Matching Pursuit（ROMP） algorithm, Sparsity Adaptive Matching Pursuit algorithm（SAMP）, Compressive Sampling Matching Pursuit（CoSaMP） algorithm.

Key words: compressed sensing, sparse representation, subspace pursuit algorithm, adaptation, regularization

摘要： 针对压缩感知中未知稀疏度信号的重建问题，提出一种新的压缩感知的信号重建算法，即自适应正则化子空间追踪（Adaptive Regularized Subspace Pursuit，ARSP）算法，该算法将自适应思想、正则化思想与子空间追踪（Subspace Pursuit，SP）算法相结合，在未知信号稀疏度的情况下，自适应地选择支撑集原子的个数，利用正则化过程实现支撑集的二次筛选，最终能实现信号的精确重构。仿真结果表明，该算法能够精确重构原始信号，重建效果优于SP算法、正则化正交匹配追踪（ROMP）算法、稀疏度自适应匹配追踪（SAMP）算法、压缩采样匹配追踪（CoSaMP）算法等。

关键词: 压缩感知, 稀疏表示, 子空间追踪算法, 自适应, 正则化