Several Methods Of Image Restoration

This paper is an overview about the image restoration methods. Image restoration are extensively applied in science, engineering, medical treatment and so on. With the development of modern science and technology, image restoration problem has become an important topic in the field of image processing.Image restoration itself is a ill-posed problem , so usually needs some regularization method to deal with the problem, this paper introduces the recent common regularization method, image restoration were transformed into a functional minimum value problem after the introduction of certain regularization.The steepest descent method, Newton method, conjugate gradient method and fixed point algorithm of solving functional minimum value problem already had more in-depth research. This paper will mainly expound the application of ADM (Alternating Direction methods) in image restoration.Firstly introduce the general degradation model of image restoration: g = Hf+ηηis additional noise , H : RN ?RN is a linear transformation(the stiffness matrix of Discrete form of blur kernel) , g is the blurred noisy image , f Is the real image , From observed image g to restore real image f usually is a ill-posed inverse problem , In order to avoid true solution f is too sensitive to noise , not depends on g continuously , We usually adopt regularization method , TV regularization method can keep image edges very well, so this paper adopts TV regularization method. TV regularization method framework usually is an unconstrained problem as below f·is the minimum point the function, which also is real image we get. In these equations n is the pixels number.(?) : R~Nâ†'R~N×R~N is a discrete version of the gradient. . 1 represents a norm on R~N×R~N, represents l 2 ?norm ,αand ? are positive real numbers .Image restoration usually was solved as an unconstrained problem above. We will also introduce a method on solving the constrained problem by alternating direction methods.The second Chapter, this paper will introduce some common regularization methods in the application of image restoration, and simple to describe the advantage and disadvantage of these methods.The third Chapter, we will introduce the general form of ADM, combined with augmented Lagrangian framework, give how to apply this method to image restoration problem, present the restore result and computing time through the numerical experiments.Finally, we present a summary and some problems we will study in the future.