Research On Image Restoration Method Based On Sparse Representation

With the development of Internet technology,images as the main media which can carry social information and the number of digital images has increased exponentially.However,in the process of acquiring and collecting images,it can be affected by the equipment and the environment easily,which causes a large amount of noise.These phenomena have a great obstacle on the subsequent research work.Therefore,image restoration technology has attracted the attention of a large number of scholars.Nevertheless image restoration technology is an ill-posed inverse problem from the mathematical point of view.The purpose of image denoising is to recover the original image from the degraded image.Since the 21st century,digital information has increased substantially,but there is less effective information in massive data.Aiming at this phenomenon,the theory of sparse representation has attracted the concern of scholars.Image restoration technology based on sparse representation has been widely used.This paper studies the image restoration algorithm based on sparse representation from three aspects:gray image denoising,color image denoising and deblurring.The main work of this paper includes:(1)In the process of image denoising,due to the influence of noise,accurate prior knowledge cannot be learned,which is difficult to obtain better sparse coefficients.Aiming at this problem,a non-convex weighted l_p norm sparse error constraint model and the corresponding gray image denoising algorithm are proposed.And through experimental analysis the optimal setting of power p in l_p norm.Firstly,the proposed algorithm decomposes the sparse coefficient solving process into two sub-problems.The generalized soft threshold algorithm is used to solve the sparse coefficient in the l_p norm,and the proxy algorithm is used to solve the sparse coefficient in the sparse error constraint.Then,the final sparse coefficient is obtained according to the mean of them.Compared with several typical gray image denoising algorithms,the proposed algorithm not only has higher PSNR and SSIM,but also has higher efficiency in running time.At the same time,it produces a better visual experience.(2)For convex optimization image restoration algorithm,because the each rank component of kernel norm is usually over-contracted.It is difficult to obtain the optimal sparse coefficient.This paper proposes a weighted l_p norm sparse error constraint(WPNSEC)model based on ADMM framework,and extends the proposed model to color image denoising and deblurring algorithms.Since the noise intensity of RGB channels is different,a weight matrix is introduced to measure the noise level of different channels.A multi-channel weighted l_p norm sparse error constraint algorithm is proposed.Then,in order to ensure that the proposed algorithm is easy to process,the multi-channel WPNSEC algorithm is transformed into an equality constraint problem and which can be solved by an alternating direction multiplier(ADMM)algorithm.The experimental results of denoising and deblurring of color images show that the multi-channel WPNSEC not only has higher PSNR,but also has better visual experience than the competing image denoising and deblurring algorithms.