Because the infrared imaging system will be disturbed by various kinds of external environment in the signal transmission and signal conversion, the infrared imaging system will produce many kinds of noise in the infrared image generated, which will lead to the decrease of the signal-to-noise ratio of the infrared image.In view of the problem that infrared images are affected by multiple types of noise,to make a new weighted coefficient based on the iteratively reweighted least squares algorithm of compressed sensing theory and combined the principle of median filtering to construction a new reconstruction algorithm.Firstly, the median filter is used to do rough denoising of infrared image.Then fine denoising by compressing the sensing sparse transformation and observation matrix to keeping the observations important information about the original signal.Finally, the denoised by reconstruction algorithm.The algorithm is simulated in MATLAB to verify the effectiveness of the algorithm.Experiments show that the visual effect of the image obtained by this algorithm is close to the original image, and it has better denoising performance in the actual scene. The peak signal-to-noise ratio is 3dB～8dB higher than the original SP algorithm and 5dB higher than the iterative weighted least square algorithm.5dB ~13dB.