An image o ften contains different levels of degradation.In order to obtain a higher qualit y image from the degraded image,different kinds of restoration methods have been proposed.Since the sparse characteristics of natural images ha ve been well revealed in the past several decades,the sparse representation based methods ar e considered as the most promising algorithms.However,the present image restoration methods base d on sparse representation cannot accurately represent small scale details of reconstructed images.To overcome this drawback,a new image restoration method which combines sparse rep resentation and matching gradient distribution is proposed.To improve the performance of th e traditional image restoration model based on sparse representation,the proposed algorithm u tilizes a parameterized hyper-Laplace model to estimate the gradient distribution of the original image.Then a global constraint is applied on the gradient distribution of images,and the h istogram specification operation is performed to match the gradient distribution.Thus th e gradient distribution of the reconstructed image is similar to that of the original image .Numerical experimental results indicate that the proposed algorithm has good recovery performance,an d can represent the image details with high accuracy.