In order to improve the efficiency of processing the large amount of data of infrared image, in this paper we develop a new infrared image processing method based on compressed sensing (CS) and simulate the method. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet), can be subjected to fewer measurements than the nominal number of pixels, and yet be accurately reconstructed. According to the properties of wavelet transform sub-bands, firstly we make wavelet transform which change the infrared image into a wavelet coefficients matrix. Acquired the features of infrared image, the characters of the wavelet coefficients can be concluded. When deeply analyzing the data of the wavelet coefficient, we can easily find the high-pass wavelet coefficients of the image are sparse enough to measure, while the low-pass wavelet coefficients are not appropriate for measure. So in this second part, only measured the high-pass wavelet coefficients of the image but preserving the low-pass wavelet coefficients. For the reconstruction, the third part, by using the orthogonal matching pursuit (OMP) algorithm, high-pass wavelet coefficients could be recovered by the measurements. Finally the image could be reconstructed by the inverse wavelet transform. The simulation proves that applying the CS theory to the realm of infrared picture can decrease the amount of data which must be collected. Besides, compared with the original compressed sensing algorithm, simulation results demonstrated that the proposed algorithm improved the quality of the recovered image significantly.