Edge Adaptive Total Variation Model For Image Deblurring

Images are an important source for people to obtain information.However,during the shooting process,the images will be inevitably affected by noise and blur,which reduces the image quality.Damaged images will cause difficulties for further image processing,therefore it is necessary to restore the original image.Image deblurring is an important branch of image restoration,which has important research value and significance.Image deblurring is a mathematically ill-posed inverse problem.The common technique for solving ill-posed problems is to find a set of well-posed problems adjacent to the original problem to approximate the original problem,which is called regularization method.Establishing an effective regularization method is a significant research content of image restoration.Hence,the key of the image deblurring model is to select a proper regularization function.The most representative regularization model is the total variation model.It is widely used in the field of image deblurring because it has the effect of protecting image edge information.In order to overcome the drawbacks of total variation model,an edge-based multiple adaptive total variation model is proposed by adding an edge adaptive parameter to the total variation regularization.The model automatically adjusts the regularization parameter based on the the local information of each pixel,which helps to better protect the edges.The alternating direction method of multipliers is employed in our model.Numerical experiments show that the proposed model outperforms many state-of-the-art image restoration models cited in paper in both peak signal noise ratio and structural similarity index.The harmonic model based on the norm of L~2has a good restoration effect on the smooth area of the image.However,its ability to diffuse in all directions is same,which causes the image edge blur.The total variation model can retain the edge well.Whereas an inevitable problem is that it will produces staircase effect in the smooth area.To alleviate the staircase effect for TV model and avoid the edges blurring for harmonic model,a hybrid regularization adaptive model based on edge detection is proposed for image deblurring.The model utilizes a spatially dependent regularization parameter to sharpen edges,total variation regularization and Tikhonov regularization can be adaptively scaling based on the local information of the each pixel.The edge information matrix will be dynamically updated with the iteration process.Numerical simulation results demonstrate that our proposed model can effectively protect the image edge while eliminating noise and blur.The recovery effect outperforms other models.