Blind Image Restoration Model And Fast Algorithm Based On The Theory Of Convex Optimization

The process of turning the degraded image into the sharp image is called image restoration. Image restoration includes image denoising, eblurring, inpainting, image enhancement and so on. Image quality degradation is mainly caused by the relative motion between the object and imaging systems, noise, imaging optics distortion, which makes it impossible to obtain accurate information on the visual effect. In recent years, image restoration algorithm has been a research focus. In order to restore a sharp image, the mathematical model of image restoration is to be set up, which is based on image degradation system and the known condition about the blurry image and prior knowledge of the shape image, and then the corresponding algorithm is deduced to estimate the sharp image. At present, the prior models of sharp images exist, which are based on 1l norm, TV norm, or ql norm. These models are widely used in image restoration, but the quality and speed of image restoration is to be improved.In this paper, a fast algorithm which aims to solve the problem about blind image restoration is proposed. The main tasks and innovations are as follows:Firstly, the reasons of image degradation are analyzed briefly, and the classic models of image degradation and image restoration are introduced, as well as some related knowledge.Secondly, as to the problem of image deblurring in image restoration, several deblurring models and algorithms with good results are described in detail. The theoretical analysis and experiments are performed. We make a comprehensive comparison on the clarity and the recovery speed of the related algorithms.Finally, we study two different blind image deblurring algorithms, and on this basis, propose a concave-convex norm ratio prior model. For the marginal distributions of real world images are no-Gaussian distribution, our analysis leads to an effective concave-convex ratio regularizer on the gradient image which only depends on the given blurry image, the fidelity term of the model based on 1l norm. In this paper, we introduce a split method, which is more convenient to find exact solution for the non-convexity of the regularizer, and we propose the thought of linear increasing trend of trade-off parameter ?. We use multi-scale analysis method to estimate the blur kernel from coarse to fine level, then use closed-form thresholding formulas to recover a sharp image. This method can obtain the correct convergence and get the sharp image in high speed with great quality during iterative process of image restoration. The experimental results verified the effectiveness of the model and the fastness of this algorithm.