有限带宽信号的双谱线比值压缩感知重构算法

摘要

为提高有限带宽信号的压缩感知( Compressed Sensing,CS)重构效率,本文提出基于双谱线比值的压缩感知重构算法.该算法充分考虑变换矩阵的正交基特性,引入无需加窗的谱校正措施,利用DFT峰值谱与次高谱线的幅度比值估计信号频率、相位及幅值参数重构出源信号.多次有限带宽信号重构实验的分析结果表明:在噪声明显的环境下,本文方法在所有仿真方法(双谱线法和l1、l2线性规划法)中误差最小,稳定性最高；若耗费相同数量的观测样本,本文算法的重构误差仅为l2线性规划法的1/15.本文算法比传统lp线性规划法的重构效率更高,同时降低了压缩感知重构所需的有限等距要求,只需提取2倍频率成分个数的谱线信息即可高概率重构信号,提高了样本的利用率.%In order to improve the Compressed Sensing reconstruction efficiency of the band-limited signal, this paper presents a reconstruction method based on double spectral lines. Considering the orthogonal basis feature of transformation matrix, this method introduces the measure of no-window spectral correcting to estimate the frequency, initial phase and amplitude parameters and reconstruct the original signal, in which the magnitude ratio of the peak and sub-peak DFT spectral samples is utilized. Comprehensive analysis of multiple band-limited signal reconstruction experiments shows that: with the same amount of samples consumed, the proposed method is characterized with the minimum error and the highest stability a-mong these 3 methods ( double spectral lines, l1, l2 linear programming) in noisy environment. And the reconstruction error of the proposed algorithm is only 1/15 of the l2 linear programming. Comparing with the conventional lp linear programming reconstruction algorithms, this method is of higher efficiency and reduces the RIP requirement of CS signal reconstruction. Moreover, it can reconstruct signal with high probability by extracting the information from the spectral lines only twice the number of signal components so that the rate of sample utilization is enhanced greatly.