The output images from a conventional 4f information optical system are characterized by their limited frequency bands

random noises and coherent noises in coexistence. Therefore

when those images are restored

it is necessary to protect image details better and to remove the noises in high frequency domain and the coherent fringes in low frequency domain. According to these characteristics

a new method is proposed to restore 4f system images and to improve the image quality. Firstly

the step response image of the 4f system is used to obtain the prior knowledge of the coherent noise

then the step response and pending images are processed to remove the high frequency random noise in contourlet domain. Finally

based on the linear characteristics of 4f system

the pixel value of the pending image divides the pixel value of step response image from point to point to remove the coherent noise. Experiments demanstrate that the method can restore images and protect image details well and its Peak Signal to Noise Ratio(PSNR)and Structural Similarity Index(SSIM) have improved by 5 db and 6%

respectively. These results show that the proposed method is suitable for 4f optical systems.