The analysis of noise reduction performance in Compressed Sensing

For the Compressed Sensing (CS) problem of noisy signal, the observation model of signal with white Gaussian noise is established and the changes of measurements caused by noise are studied. It is found that, the sparse manifestation of signal and the process of obtaining measurements have the function of noise reduction. In computer simulation, Gaussian random matrix and Orthogonal Matching Pursuit (OMP) algorithm are used to calculate the trend of reconstruction error along with the number of measurements in different Signal to Noise Ratio (SNR). The results of simulation show that in a certain range of SNR, there are always a certain number of measurements to make the error of reconstructed signal less than the error of noisy signal itself. At last, the empirical formula among Matching Rate, SNR and the number of measurements is fitted by experimental data, which contributes to the selection of optimal number of measurements.