A algorithm which uses the compensation factor to eliminate nonlinear errors was proposed to reduce the nonlinear errors caused by sudden change of background in the imaging system based on compressed sensing. The compensation factor was calculated from the mean value of measured data under different background. The simulation results show that the proposed algorithm improve the peak signal to noise ratio of reconstructed image from 29.5 dB to 62 dB when the background noise change as many as 300 times during 900 times sampling. The reconstructed image is more readable and the imaging system is more robust with the proposed algorithm.