A Compressed Sensing Band-limited Signal Reconstruction Algorithm based on the Ratio of Double Spectral Lines

 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 among 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.