Abstract: Because of light scattered by the suspended particles in the atmosphere,photographs taken in the foggy day look gray and are lack of visibility.In order to unveil the clear image's structures and colors,we propose a new algorithm based on the atmosphere scattering model using a single image and the image sparsity prior in Bayesian framework.The fog removal result is optimized under the constraint of the prior of the image gradient sparsity and the noise in the foggy image being the normal distribution with zero mean,and then the optimization function is computed using the IRLS algorithm.In our experiments,the algorithm has a good effect on restoring the clear image's contents and preserving the image's true colors.The noise in the output image is very weak that has advantage for many applications.