Under the framework of compressed sensing theory, the greedy algorithm achieves good reconstruction performance with known signal sparsity. However, unknown sparsity of sparse signals in practical applications brings obstacles for signal reconstruction. Specifically, the conventional sparsity adaptive adjustment algorithm takes long time to finish the reconstruction, and the accuracy of reconstruction is not good enough. To solve this problem, this paper proposes a new matching pursuit reconstruction algorithm based on bidirectional sparsity adaptive adjustment and weak selection of atoms (BSA-WSAMP). In this algorithm, the optimization strategy for atom weak selection is employed to update the support set, and the idea of "zoom" bidirectional variable step-size is applied to achieve the sparsity adaptive adjustment. Based on this, the number of iterations can be reduced effectively, and the accurate reconstruction of the sparse signal is obtained. Simulation results indicate that the proposed BSA-WSAMP algorithm achieves better adaptive characteristic of the sparsity, higher reconstruction quality, lower reconstruction complexity, and less reconstruction time than some existing reconstruction algorithms.

在压缩感知理论的框架下，贪心算法在已知信号稀疏度的情况下实现了良好的重构性能。然而，实际应用中稀疏信号的未知稀疏性给信号重建带来了障碍。具体而言，传统的稀疏自适应调整算法完成重建需要很长时间，并且重建的精度不够好。针对这一问题，本文提出了一种基于双向稀疏自适应调整和原子弱选择的匹配追踪重建算法（BSA-WSAMP）。该算法采用原子弱选择优化策略更新支持集，并采用“缩放”双向可变步长的思想实现稀疏自适应调整。基于此，可以有效减少迭代次数，得到稀疏信号的准确重构。仿真结果表明，与现有的一些重建算法相比，所提出的BSA-WSAMP算法具有更好的稀疏自适应特性、更高的重建质量、更低的重建复杂度和更少的重建时间。