Variable decomposition in total variant regularizer for denoising/deblurring image

The aim of image restoration is to obtain a higher quality desired image from a degraded image. In this strategy, an image inpainting methods fill the degraded or lost area of the image by appropriate information. This is performed in such a way so that the resulted image is not distinguishable for a casual person who is not familiar with the original image. In this paper, the various images are degraded with different ways: 1) the blurring and adding noise in the original image, and 2) losing a percentage of the pixels of the original image. Then, the proposed method and other methods are performed to restore the desired image. It is required that the image restoration method use optimization methods. In this paper, a linear restoration method is used based on the total variation regularizer. The variable of optimization problem is decomposed, 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 than other methods.