Research On Image Restoration Algorithm Based On Overlapping Combined Sparse Regular Terms

Due to the imperfection of an imaging system and environmental equipment,a recorded image may be inevitably degraded during the process of image capture,transmission,and storage.Therefore,image restoration is one of the most fundamental issues in the field of digital image processing,and it plays a very important role in many image processing applications.Traditional total variation(TV)is widely used in image restoration problems for its capability to preserve image edges.However,the TV model tends to transform smooth regions(ramps)into piecewise constant regions(stairs),so it yields the staircase effects in the restoration process.In order to improving the quality of image restoration,this paper introduces overlapping group sparsity regularization term based on total variation.Besides,this paper establishes the corresponding image restoration model in two aspects: image denoising and image deblurring.The main work of this paper is as follows:Firstly,to extend the traditional total variation model,this paper proposes a high-order total variation model with overlapping group sparsity,it promotes pixel-level gradient information to high-order overlapping group sparse gradient information.This new model not only inherits the characteristic of classical total variation,such as preserving image edges and other detail information,but also makes full use of the information of high-order derivative to preserve the image discontinuity to suppress the staircase effects.Secondly,traditional total variation model merely considers gradient information in the vertical and horizontal directions,but ignores the gradient neighborhood information of the image.Then,four-directional total variation introduces more gradient information in the directions.In view of this,this paper proposes a four direction total variation with overlapping group sparsity.The new model combines gradient information of each pixel in four directions(vertical,horizontal,diagonal and back-diagonal)to form a new sparse regularize constraint,that is,non-separated group gradient.Therefore,it makes full use of gradient information in four directions,improves the difference between the smooth region and the edge region,and greatly reduces the staircase artifacts.Then,in order to solve the optimization problem of the two proposed restoration models effectively,this paper uses alternating direction method of multipliers(ADMM)algorithm to divide the constrained optimization problem into separate subproblems.Assuming that the image satisfies the periodic boundary conditions,this paper uses the two-dimensional fast Fourier transform and control minimization algorithm to solve the subproblems alternately.Finally,to demonstrating the effectiveness and superiority of the proposed models,the proposed models are compared with other state-of-the-art image restoration models.Moreover,the peak signal-to-noise ratio(PSNR),structural similarity(SSIM)and calculation time are introduced to quantitatively analyze the quality of image restoration.Experiments show that the proposed two models can achieve better restoration results than other models in terms of subjective visual effect and objective index evaluation.