Abstract:An image restoration based on Radon transform and minimizing variational function was proposed, inorder to restore the blurring and noisy images by photography. The proposed algorithm firstly de-noised the blurring and noisy image by directional filter, then estimated the spread point function based on Radon transform which can eliminate error of the estimation due to the directional filter. Since then, the original image was de-burred by de-convolution with the spread point function. Finally, the de-blurred image was further de-noised by the variational function with L0-norm regularization. By experiments, the proposed algorithm can restore blurring and noisy images.