Compressed sensing (CS) is a new theory for sampling and recovering signal-based sparse transformation. This theory could help us to acquire complete signal at low cost. Therefore, it also satisfies the requirement of low-cost sampling since bandwidth and capability of sampling is not sufficient. However, wireless sensor network is an open scene, and signal is easily affected by noise in the open environment. Specially, CS theory indicates a method of sub-Nyquist sampling which is effective to reduce cost in the process of data acquirement. However, the sampling is “imperfect”, and the corresponding data is more sensitive to noise. Consequently, it is urgently requisited for robust and antinoise reconstruction algorithms which can ensure the accuracy of signal reconstruction. In the article, we present a proximal gradient algorithm (PRG) to reconstruct sub-Nyquist sampling signal in the noise environment. This algorithm iteratively uses a straightforward shrinkage step to find the optimum solution of constrained formula, and then restores the original signal. Finally, in the experiment, PRG shows excellent performance comparing to OMP, BP, and SP while signal is corrupted by noise.

压缩感知（CS）是用于采样和恢复基于信号的稀疏变换的新理论。该理论可以帮助我们以低成本获取完整的信号。因此，由于带宽和采样能力不足，它也满足了低成本采样的要求。但是，无线传感器网络是一个开放的场景，在开放的环境中，信号容易受到噪声的影响。特别地，CS理论指出了一种亚奈奎斯特采样方法，可有效降低数据采集过程中的成本。但是，采样是“不完美的”，并且相应的数据对噪声更敏感。因此，迫切需要鲁棒且抗噪的重建算法，以确保信号重建的准确性。在文章中 我们提出了一种近端梯度算法（PRG）在噪声环境中重构次奈奎斯特采样信号。该算法反复使用简单的收缩步骤来找到约束公式的最佳解，然后恢复原始信号。最后，在实验中，PRG与OMP，BP和SP相比表现出出色的性能，而信号却被噪声破坏了。