Nonconvex Minimization Method Based On Wavelet Frame For Image Restoration

Image restoration is mainly for analysing and processing the observed de?graded images,so that the restored images satisfy the visual requirements.Image restoration mainly includes image denoising,image deblurring and so on.This paper primarily focuses on the issues,including the establishment of models,the design of algorithms,the analysis of convergence theory and the verification of experiments to solve related problems.The following are the main research contents and innovation points in this paper.1.A fast alternating minimization method based on split Bregman and wavelet frame is proposed to perform image deblurring and denoising,which is deblurring and denoising alternately.Two models are built and two algorithms are given.For the first method.The l1 minimization based on the analysis sparse representation method is used as doblurring step,and the TV norm is used as the penalty term in the noise step.For the second method,we take into account that the fast iterative shrinkage threshold algorithm(FISTA)has the advantages of simple encoding and fast convergence,and use l1 norm instead of TV term to denoise.The two methods mentioned above have their own advantages.The experimental results show that the method based on TV term is more effective to some extent.but the l1 norm based on FISTA method is more convenient to operate.The split Bregman method is used to solve the minimization problem based on the analysis of sparse representation.Experiments show that our mod-ified alternating minimization method has good effects on dealing with different blurs and Gaussian noise.and shows obvious advantages when compared with related algorithms.2.The l0 regularization based on the wavelet frame and the proximity al-gorithm for the alternate approach is proposed to remove the blur and noise altrnately.In the deblurring step.the sparse representation based on l0 regu-larization is used,and the TV term is used as a penalty in the denoising step.Here we use the mean double angmented Lagrange(MDAL)method for solving l0 minimization problem based on wavelet frame to achieve deblurring effect,and the proximity algorithm is to denoise the previous deblurred image.Experiments show that our improved model and combined algorithm has good effect on deal-ing with different blur and Gaussian noise.Compared with related algorithms,the superiority of the proposed method is verified.3.The image restoration problem can be described as for finding a minimum value of suitable objective function.This objective function consists of two parts,the data fidelity term and the regularization term.This paper introduces the non-convex metric l1-?l2(??1)in compressed sensing(CS)theory,which is the weight difference between the l1 norm and the l2 norm,and wavelet frame theory is combined as a regulation term for image restoration.We consider different types of noise.Gaussian noise is processed by using l2 norm as data fidelity;impulse noise is processed by using l1 norm as data fidelity;mixed Gaussian impulse noise is processed by mixing l1/l2 norm.This method is called the the l1-?l2 minimization method based on framelet.Here.the proposed minimization models are solved by the alternating direction multiplier method(ADMM).The process of ADMM algorithm is described in detail,and the convergence analysis of the result algorithm is given.Here we recover images degraded by different types of blur and Gaussian noise,impulse noise and mixed noise.The experimental results show that the wavelet frame-based l1-?l2 is proposed in this chapter.both quantitatively and visually.the minimization model superior to the existing related methods.4.Considering that image sharpening can highlight the details of the image,the article considers constructing an inage sharpening operator,and based on the sharpened image,we introduce a new imago restoration model.The mod-el is based on the data fidelity of the l2 norm and the regularization term of the l1 norm based on the wavelet frame and the fit term on the l1 norm of the sharpened image.To solve the minimization model.we use the alternating direc-tion multiplier method(ADMM).split the problem into several sub-problems,and solve it simply and efficiently.Experimental restults show that the proposed minimization method is robust copared to existing methods.