压缩感知理论提供了一种全新的信号获取方式：引入信号的稀疏性，利用少量观测值，通过重构算法实现信号的高精度重构。构建快速、稳定的重构算法是压缩感知理论的主要研究方向之一。为了解决子空间追踪算法依赖于稀疏度的先验信息和重构质量较差的问题，提出一种改进的自适应子空间追踪算法。算法在选择原子的过程中，引入弱选择标准自适应地选择初始候选集，接着通过正则化过程对初始候选集中的原子进行筛选，算法在选择最终支撑集过程中，可以自适应调节支撑集原子个数。应用一维随机信号和二维图像进行重构实验，测试算法的稳定性、重构精度和重构时间，与正交匹配追踪算法、子空间追踪算法、正则化正交匹配追踪算法和稀疏度自适应匹配追踪算法进行对比实验，实验结果表明所提算法可以实现信号的高精度重构，重构稳定性和重构精度与同类算法相比有明显提升。

Compressed sensing theory provides a new method for signal acquisition: it introduces the sparsity of the signal and uses a small amount of observed values to reconstruct the signal precisely by using a reconstruction algorithm. Constructing a fast and stable reconstruction algorithm is one of the primary research directions for compressed sensing theory. The subspace pursuit(SP) algorithm relies on the prior information of sparsity and the poor reconstruction quality. To solve this problem, a modified sparsity adaptive subspace pursuit(MSASP) algorithm is proposed. While selecting the atom, the algorithm first selects the initial candidate set with the weak selected standard and then selects the atoms in the initial candidate set through the regularization process. While selecting the final support set, the algorithm can adjust the number of support set atoms adaptively. By performing experiments with one-dimensional random signals and two-dimensional images, the reconstruction stability, reconstruction precision, and reconstruction time of the algorithm were tested. The algorithm is then compared with the orthogonal matching pursuit, SP, regularized orthogonal pursuit, and sparsity adaptive matching pursuit algorithms. The experimental results show that the proposed algorithm can reconstruct the signal precisely while displaying clear improvements in terms of reconstruction stability and precision over the other algorithms.