The Preconditioned Fast Algorithms For Image Restoration

With the constant improvement of the electronic technology and computer technology,the digital image processing goes into a period of rapid development.Image restoration is widely used and plays an important role in the area of image processing.Since image denoising is the basis of image restoration,the research on image denoising has very important practical significance.In recent works several authors considered the three denoising models with the L₁ fidelity term,the L₂ fidelity term and the combined L₁ and L₂ fidelity term,and they used the fast Fourier transform?FFT?algorithm which can only use periodic boundary conditions.In this paper we combined the augmented Lagrangian method?ALM?and the symmetric Red-Black Gauss-Seidel?SRBGS?method to propose three corresponding preconditioned fast algorithms that are suitable for different boundary conditions.Experimental results show that the proposed algorithms are effective and the model with the combined L₁ and L₂ fidelity term demonstrates more advantages in efficiency and accuracy than the other two models with the L₁ and L₂ fidelity term,respectively.Due to the importance of edge detection in image processing,we proposed a new edge detection model with the combined L₁ and L₂ fidelity term and showed an efficient algorithm which can be used to solve this minimum model based on a fixed-point iterative method and the split-Bregman method.Besides,experimental results show that the proposed edge detection model and algorithm can not only control different pure noisy images,even mixed noisy images,but also get good detected edges.Meanwhile,the proposed edge detection model and algorithm also present that it is robust,effective and accurate.