一种变步长稀疏度自适应子空间追踪算法

A Variable Step Size Sparsity Adaptive Subspace Pursuit Algorithm

针对压缩感知(Compressive sensing,CS)中未知稀疏度信号的重建问题,本文提出一种变步长稀疏度自适应子空间追踪算法.首先,采用一种匹配测试的方法确定固定步长,然后以该固定步长与变步长方式相结合,通过不同支撑集原子个数下的重建残差变化确定信号稀疏度,算法采用子空间追踪方法确定相应支撑集原子,并完成原始信号准确重建.实验结果表明,与同类算法相比,该算法可以更准确重建原始信号,且信号稀疏度值较高时,运算量低于同类算法.

A novel variable step size sparsity adaptive subspace pursuit algorithm is proposed to rebuild the sparse signals with unknown sparsity in compressive sensing. Firstly, the initial fixed step size is obtained by matching test,which is combined with the variable step size method. Then, the sparsity is accurately estimated according to the change of signal rebuilding residual error under vary support set. Subspace pursuit algorithm is used to determine the support set and exactly rebuild the sparse signal. Simulation results show that the proposed algorithm is competitive in recovering accuracy and running speed, compared to other similar algorithms, when sparsity is large.