基于SWCoSaMP算法的稀疏信号重构

压缩感知(compressed sensing, CS)稀疏信号重构本质上是在稀疏约束条件下求解欠定方程组。针对压缩感知匹配追踪(compressed sampling matching pursuit, CoSaMP)算法直接从代理信号中选取非零元素个数两倍作为支撑集，但是不存在迭代量化标准，本文提出了分步压缩感知匹配追踪(stepwise compressed sampling matching pursuit, SWCoSaMP)算法。该算法从块矩阵的逆矩阵定义出发，采用迭代算法得到稀疏信号的支撑集，推出每次迭代支撑集所对应重构误差的L-2范数闭合表达式，从而重构稀疏信号。实验结果表明和原来CoSaMP算法相比，对于非零元素幅度服从均匀分布和高斯分布的稀疏信号，新算法具有更好的重构效果。 

Sparse Signal Recovery Based on Stepwise Compressed Sampling Matching Pursuit

The compressed sensing(CS) sparse signal recovery is actually solving a system of underdetermined linear equations within the sparse nature of its solution.The compressed sampling matching pursuit(CoSaMP) algorithm directly selects support sets of twice nonzero elements number from the maximizing signal proxy without a quality criterion for every iterative time.The stepwise compressed sampling matching pursuit(SWCoSaMP) algorithm is proposed in this paper,which uses the iterative method to obtain the sparse signal support set.It acquires the sparse signal support set by the definition of the block matrix inversion so that reconstructs the sparse signal.The recovery error’ s L-2 norm is also given corresponding with the support set for every iterative time.Compared with CoSaMP,simulative results show that the new algorithm has a good recovery performance for the sparse signal whose nonzero values are distributed uniform or Gaussian.