Blurred Image Restoration Using A Regularized Linear Programming Model

Context: Minimization problems in the sense of least squares have constantly been used in the restoration of blurred images. They are characterized by their sensitivity to outliers, which significantly affects affecting the quality of the restored image relevantly. Since the L-1-norm is less sensitive to outliers, the image deblurring problem is posed as a linear programming problem.Method: An interior point method is used to solve the linear programming problem.This article presents the adaptation of regularization techniques of the image sought and its derivative to the problem of linear programming. A comparative study with other restoration methods under different types of image blurring is conducted.Results: The proposed method leads to remarkable improvements in the recovered images. Numerical experiments show that the linear programming method works much better than those proposed in the literature, in terms of PSNR and SSIM values as well as in the visual quality of the reconstructed images.Conclusions: The regularized linear programming problem can be effectively used as a mathematical model of the image deblurring problem. For future work, there are plans to study of the automatic selection of regularization parameters and restoration solutions without prior knowledge of the blur kernel.