Image Restoration Based On Numerical Algebraic Method

In the field of digital image processing, image recovery is a very important researchdirection in real life and in possession of a wide range of applications and markets, such asthe vehicle identification monitoring systems, satellite remote sensing image processingsystem, Astronomical imaging system, the video processing system, as well as militaryimage processing system, those are all dependent on the digital image restoration tech-niques.The image quality will be degradated by the blur and distortion interference in theformation or transfer process, and the noise would been added in the original images ow-ing to the device’s low precision or the environmental disturbances between the devicesand the image-taking point. Image restoration technique aims to reduce or remove thisdegradation effect and try to get the original image. In recent years, people’s require-ment to the image quality gradually improves, for instance, color images instead of thegrayscale images, the3D images slowly in stage. At the same time, the image restorationtechnology must to be risen, which is both a challenge and an opportunity to researchersin this field.The image restoration techniques need to break the two problems: first, using ac-curate mathematical model to simulate the process of image degradation; second, usingfeasible and efficient mathematical methods to solve the mathematical model.For the first problem, the domestic and foreign researchers proposed a series of ef-fective, more and more applicable models. The LS model is the early model, with deeplyresearching, the current popular model is the regularization model, the ROF model is oneof the most popular regularization model. This paper proposes a high-order total varia-tion regularization model based on the previous studies, the model takes into account thehigh-order differential information of the image, thus it can simulate the image degrada-tion process better, and the existence and convergence of the proposed model is provided.For the second problem, the scholars in the field of numerical algebra have proposed alot of methods, that is, the directly solving technologys, the iterative methods, subspacemethods. This paper presents a augmented Lagrangian method, which is based on theoptimization theory and the Lagrange multiplier strategy. Numerical experiments show that the proposed new model and new method have better restoration effect and fastercomputing speed than some of the current popular models and methods.