Research On Image Reconstruction Algorithm Based On Sparse Representation And Low Rank Model

Digital multimedia technology has been ubiquitous and widely used in many fields since human society entered the 21st century.As a kind of important product of dig-ital multimedia technology,image has become the main carry of the transmission of the information.However,due to the influence of shooting equipment and man-made misoperation in the processing of image capture,compression and transmission,the ob-tained images are often degraded,which bring much inconvenience to people's work and life.Therefore,how to recover the original images from degraded ones is still a hot topic.Image restoration is essentially an ill-posed inverse problem in mathematics.By using the prior models of natural images to regularize the real solution space,the ill-posed inverse problem is translated into a well-posed and visual-stable solution is obtained.In this paper,from the point of sparse representation and low rank model,we mainly focus on research topic on four image restoration tasks,including image denoising,image inpainting,image deblurring and image compressive sensing(CS)recovery.The proposed algorithms are demonstrated to have superior performance in practical applications.The main work of this paper is shown as follows.First,a new image CS recovery algorithm based on adaptive sparse nonlocal reg-ularization model is proposed.Traditional image CS recovery methods exploited the fixed bases(i.e,DCT,wavelet and Curvelet)for the entirety signal,which are irrespec-tive of the non-stationary of natural signals and cannot obtain high enough degree of sparsity,thus leading to a poor reconstruction performance.Bearing the above concern in mind,we propose an adaptive sparse nonlocal regularization(ASNR)model for im-age CS recovery.In ASNR,an effective self-adaptive dictionary learning method is used to greatly reduce artifacts and the loss of fine details.Furthermore,the image sparse nonlocal(or nonlocal self-similarity)priors are integrated into the regulariza-tion term,thus ASNR can effectively enhance the quality of the image CS recovery.Experimental results demonstrate that the proposed ASNR can effectively reconstruct fine structures and suppress visual artifacts,and outperform state-of-the-art methods in terms of both the PSNR and visual measurements.Second,a novel image denoising algorithm based on group sparsity residual con-straint model is proposed.Nonlocal image representation has been successfully used in image denoising.However,most existing methods only consider the nonlocal self-similarity(NSS)prior of degraded observation image,and few methods use the NSS prior from natural images.In this paper,we propose a novel method for image denois-ing via group sparsity residual constraint(GSRC).Different from the previous NSS prior-based denoising methods,two kinds of NSS prior(e.g.,NSS priors of noisy im-age and natural images)are used for image denoising.In particular,to enhance the performance of image denoising,the group sparsity residual is proposed,and thus the problem of image denoising is translated into reducing the group sparsity residual.Because the groups contain a large amount of NSS information of natural images,to reduce the group sparsity residual,we obtain a good estimation of the group sparse coefficients of the original image by the external NSS prior based on Gaussian Mix-ture Model(GMM)learning,and the group sparse coefficients of noisy image are used to approximate the estimation.Experimental results demonstrate that the proposed GSRC not only outperforms several state-of-the-art methods,but also delivers the best qualitative denoising results with finer details and less ringing artifacts.Third,we propose a scheme to analyze the group sparsity based on the rank min-imization methods.Sparse coding has achieved a great success in various image pro-cessing studies.However,there is not any benchmark to measure the sparsity of image patch/group because the sparse discriminant conditions cannot keep unchanged.Bear-ing the above concern in mind,this paper analyzes the sparsity of group based on the strategy of the rank minimization.Firstly,an adaptive dictionary is designed for each group.Then,we prove that group-based sparse coding is equivalent to the rank mini-mization problem,and thus the sparse coefficients of each group can be measured by estimating the singular values of each group.Based on that conclusion,four nuclear norm minimization methods including the standard nuclear norm minimization(NN-M),the weighted nuclear norm minimization(WNNM),Schatten p-norm minimization(SNM)and the weighted Schatten p-norm minimization(WSNM)are used to analyze the sparsity of each group and WSNM is found to be the closest solution to the re-al singular values of each group.Therefore,WSNM can be equivalently turned into a non-convex weighted lp-norm minimization problem in group-based sparse coding.Experimental results on two image restoration tasks:image inpainting and image CS recovery,show that the proposed scheme is feasible and outperforms existing state-of-the-art reconstruction methods both quantitatively and qualitatively.Fourth,a novel image denoising algorithm via non-convex weighted lp minimiza-tion based group sparse representation framework is proposed.In the past,convex optimization with sparsity-promoting convex regularization was usually regarded as a standard scheme for estimating sparse signals in noise.However,using convex regular-ization cannot still obtain the correct sparsity solution under some practical problems including image inverse problems.Bearing the above concern in mind,we propose a non-convex weighted lp minimization based group sparse representation(GSR)frame-work for image denoising.To make the proposed scheme tractable and robust,the generalized soft-thresholding(GST)algorithm is adopted to solve the non-convex lp minimization problem.In addition,to improve the accuracy of the nonlocal similar patch selection,an adaptive patch search(APS)scheme is proposed.Experimental results demonstrate that the proposed approach not only outperforms many state-of-the-art denoising methods,but also results in a competitive speed.Finally,a novel image restoration algorithm via non-convex weighted lp nucle-ar norm based ADMM framework is proposed.Since the matrix formed by nonlo-cal similar patches in a natural image is of low rank,the nuclear norm minimization(NNM)has been widely used in various image processing studies.Nonetheless,the nuclear norm is a l1-norm of the singular values in essence and it is well known that l1-norm has a shrinkage effect and results in a biased estimator.This means NNM that over-shrinks the rank components and treats the different components equally is infeasible,and thus it cannot approximate the matrix rank accurately enough.To alle-viate the above-mentioned limitations of the nuclear norm,in this paper we propose a new method for image restoration via the non-convex weighted lp nuclear norm mini-mization(NCW-NNM),which is able to more accurately enforce the image structural sparsity and self-similarity simultaneously.Experimental results on various types of image restoration problems,including image deblurring,image inpainting and image compressive sensing(CS)recovery,demonstrate that the proposed method outperforms many current state-of-the-art methods in both the objective and the perceptual qualities.