In order to restore high-quality and sharp image from motion blurred images, the coded exposure imaging technology is adopted. Different from the shutter keeping constant open in traditional camera, the shutter of coded exposure camera is in the conversion between on and off. The high frequency information of the target is effectively preserved, since the fast conversion of code in time domain is equivalent to broadband filter in frequency domain. To obtain the sharp image from the image by coded exposure, image restoration and blurred kernel estimation are recovered based on L ₀ regularization, which can preserve the high frequency details. The sharp image is rebuilt by iterative updating of the restored image and the blurred kernel. Experiments on synthetic and actual images show that the proposed method has good image restoration effect for deblurring caused by various motions.