The aim of image restoration is to obtain a higher quality desired image from a degraded image. In this strategy, an image inpainting method fills the degraded or lost area of the image by appropriate information. This is performed in such a way so that the obtained image is undistinguishable for a casual person who is unfamiliar with the original image. In this paper, different images are degraded by two procedures; one is to blur and to add noise to the original image, and the other one is to lose a percentage of the pixels belonging to the original image. Then, the degraded image is restored by the proposed method and also two state-of-art methods. For image restoration, it is required to use optimization methods. In this paper, we use a linear restoration method based on the total variation regularizer. The variable of optimization problem is split, and the new optimization problem is solved by using Lagrangian augmented method. The experimental results show that the proposed method is faster, and the restored images have higher quality compared to the other methods.