基于压缩感知的正则化子空间追踪算法

Regularized Subspace Pursuit Based on Compressive Sensing

压缩感知理论是一种新的在采样的同时实现压缩的采样过程,只要被采样信号是稀疏或可压缩的,就可以保证精确重建。通过研究总结已有的贪婪追踪类重建算法,提出了一种正则化子空间追踪算法(Regularized Subspace Pursuit,RSP)。正则化正交匹配追踪算法(Regularized Orthogonal Matching Pursuit,ROMP)的正则化方法对原子的能量分级思想,对信号的重建精度和重建速度有很大影响。首先对该方法的不合理性进行改进,然后将改进的正则化步骤引入到子空间追踪算法(Subspace Pursuit,SP)中,最终达到对原始信号的快速精确重建。实验仿真表明,该算法比SP算法更高效,更具有实际应用意义。

Compressive sensing theory is a new methodology to achieve compression while sampling. The sampled signal is reconstructed as long as the signal is sparse or compressible. Based on the research and summarization of the existing greedy pursuit algorithms, this paper presents a new Regularized Subspace Pursuit （RSP）. The idea of atomic energy classification of regularization method in Regularized Orthogonal Matching Pursuit （ROMP） has great influence on the accuracy and speed of the signal reconstruction. Firstly, the irrationality of this method is improved, and then this improved method is introduced to Subspace Pursuit （SP） ultimately leads to exact and fast reconstruction of the original signal. The experimental results show that RSP is more efficient and practical significance than SP.