基于一次投影子空间追踪的压缩感知信号重构

为了降低信号重构算法的复杂度，实现对稀疏度未知信号的重构，提出了一种基于一次投影子空间追踪(OPSP)的信号重构方法。首先根据约束等距性质确定信号稀疏度的上下界，并将最接近上下界中值的整数作为稀疏度的估计值；然后在子空间追踪(SP)算法的框架下，去掉了迭代中观测向量在支撑集上的投影过程，降低了算法的复杂度。为了更准确地衡量算法的重构性能，提出用完整信号的重构概率作为衡量算法重构性能的指标。与传统的SP算法相比，所提算法可以重构稀疏度未知的信号，且重构时间短，重构概率高。仿真结果验证了该算法的有效性。

One projection subspace pursuit for signal reconstruction in compressed sensing

In order to reduce the complexity of signal reconstruction algorithm, and reconstruct the signal with unknown sparsity, a new algorithm named One Projection Subspace Pursuit (OPSP) was proposed. Firstly, the upper and lower bounds of the signal's sparsity were determined based on the restricted isometry property, and the signal's sparsity was set as their integer middle value. Secondly, under the frame of Subspace Pursuit (SP), the projection of the observation onto the support set in each iteration process was removed to decrease the computational complexity of the algorithm. Furthermore, the whole signal's reconstruction rate was used as the index of reconstruction performance. The simulation results show that the proposed algorithm can reconstruct the signals of unknown sparsity with less time and higher reconstruction rate compared with the traditional SP algorithm, and it is effective for signal reconstruction.