A new image restoration method by Gaussian smoothing with L1 norm regularization

The search for efficient image restoration method is still a fundamental problem in image processing. Gaussian smoothing is an important linear filter smoothing method which is widely used in image denoising problem. However, outliers often remain in the edges of the recovered images obtained by linear filter smoothing. In this paper, we propose a new method which combines the Gaussian filter smoothing with L₁ norm for outliers removal together for image restoration. An alternating minimization algorithm is designed to solve the proposed model. Extensive experimental results show that the proposed model is efficient for image restoration, and it greatly improves the image restoration quality in terms of both the visual effects and quantity results comparing to the Gaussian smoothing method.