A New Image Restoration Method By Gaussian Smoothing With L₁Norm Regularization

Image restoration is a fundamental and important problem in image processing. The filtering methods and regularization methods are widely used in image restoration. Fil-tering method is a class of linear smoothing methods. Its drawback is that if the filtering effect is strong, the restored image will be over smooth and a lot of details will be lost; if the filtering effect is weak, some outliers in the restored image can’t be removed and still remain in the restored image. Regularization method for image restoration is to ob-tain the restored image by solving an optimization problem, the cost function is usually established based on the statistics characteristics of image noise and the choice of the reg-ularization term. The total variation regularization can remove noise and maintain image edges well. In this thesis, we first introduce some filtering methods and regularization methods for image restoration. And then by using the good feature of Li norm that can remove the residual outliers effectively, we design a image restoration method based on L\norm and gaussian filtering smoothing. An alternating iterative method is constructed to solve the new model. Numerical experiment results show that the proposed model is an effective image restoration method and greatly improves the quality of image restoration in both visual effect and quality results compared with gaussian smoothing method.