基于自适应滤波的压缩感知重构方法

A Compressive Sensing Reconstruction Method Based on Adaptive Filtering Framework

自适应滤波框架中,滤波器的抽头系数可以利用特定的自适应算法达到近似维纳解,从而使滤波器的输出误差达到最小。将这个框架应用到压缩感知重构信号中,信号的稀疏系数等效为滤波器系数权值向量,从而可获得最佳的稀疏系数,以高概率重构信号。本文介绍了已有学者研究出的一种L0最小均方算法(L0-LMS),该算法中引入零引力项加快了权矢量向稀疏解收敛的速度,保证解的稀疏性。通过仿真可知,基于自适应滤波算法重构稀疏信号的性能较好,甚至优于压缩感知中常用的OMP算法。

In adaptive filtering framework,the filter tap coefficients of the adaptive algorithm can be used to approximate a particular Wiener solution,so that error of the filter output can be to minimum.This framework will be applied to the compressed sensing signal reconstruction,sparse coefficients of the signal is equivalent to the weight vector to get the best of the sparse coefficient with high probability reconstructed signal,This article describes some academics have already developed a L0 least mean square algorithm(L0-LMS),the algorithm is introduced zero-weight vector to speed up the sparse rate of convergence and ensure the sparsity of the solution.The simulation shows that adaptive filtering algorithm based on sparse signal reconstruction performance is better than OMP which is the commonly algorithm used in the compressed sensing.