基于压缩感知信号重建的自适应空间正交匹配追踪算法

Adaptive Space Orthogonal Matching Pursuit Algorithm for Signal Reconstruction Based on Compressive Sensing

传统的奈奎斯特采样定理规定采样频率最少是原信号频率的两倍,才能保证不失真的重构原始信号,而压缩感知理论指出只要信号具有稀疏性或可压缩性,就可以通过采集少量信号来精确重建原始信号。在研究和总结已有匹配算法的基础上,提出了一种新的自适应空间正交匹配追踪算法(Adaptive Space Orthogonal Matching Pursuit,ASOMP)用于稀疏信号的重建。该算法在选择原子匹配时采用逆向思路,引入正则化自适应和空间匹配的原则,加快了原子的匹配速度,提高了匹配的准确性,最终实现了原始信号的精确重建。最后与传统MP和OMP算法进行了仿真对比,结果表明该算法的重建质量和算法速度均优于传统MP和OMP算法。

In order to well ensure reconstruction of the original signal,the traditional Nyquist sampling theorem requires that the sampling rate must be twice as much the highest frequency of the original signal at least,which causes a tremendous amount of calculation and the waste of resources.But the compressive sensing theory describes that we can reconstruct the original signal from a small amount of random sampling as long as the signal is sparse or compressible.Based on the research and summarization of the traditional matching algorithm,this paper presented a new adaptive space orthogonal matching pursuit algorithm（ASOMP） for the reconstruction of the sparse signal.This algorithm in-troduces an regularized adaptive and spatial matching principle for the choice of matching atoms with reverse thinking,which accelerates the matching speed of the atom and improves the accuracy of the matching,ultimately leads to exact reconstruction of the original signal.Finally,we compared the ASOMP algorithm with the traditional MP and OMP algorithm under the software simulation.Experimental results show that the ASOMP reconstruction algorithm is superior to traditional MP and OMP algorithm on the reconstruction quality and the speed of the algorithm.