As synthetic aperture radar（SAR） has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nucl...As synthetic aperture radar（SAR） has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nuclear norm minimization（WNNM） is proposed. To implement blind de-noising, the accurate estimation of noise variance is very important. So far, it is still a challenge to estimate SAR image noise level accurately because of the rich texture. Principal component analysis（PCA） and the low rank patches selected by image texture strength are used to estimate the noise level. With the help of noise level, WNNM can be expected to SAR image de-noising. Experimental results show that the proposed method outperforms many excellent de-noising algorithms such as Bayes least squares-Gaussian scale mixtures（BLS-GSM） method, non-local means（NLM） filtering in terms of both quantitative measure and visual perception quality.展开更多
Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image ...Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.展开更多
Non-convex methods play a critical role in low-rank tensor completion for their approximation to tensor rank is tighter than that of convex methods.But they usually cost much more time for calculating singular values ...Non-convex methods play a critical role in low-rank tensor completion for their approximation to tensor rank is tighter than that of convex methods.But they usually cost much more time for calculating singular values of large tensors.In this paper,we propose a double transformed tubal nuclear norm(DTTNN)to replace the rank norm penalty in low rank tensor completion(LRTC)tasks.DTTNN turns the original non-convex penalty of a large tensor into two convex penalties of much smaller tensors,and it is shown to be an equivalent transformation.Therefore,DTTNN could take advantage of non-convex envelopes while saving time.Experimental results on color image and video inpainting tasks verify the effectiveness of DTTNN compared with state-of-the-art methods.展开更多
Face hallucination via patch-pairs leaning based methods has been wildly used in the past several years. Some position-patch based face hallucination methods have been proposed to improve the representation power of i...Face hallucination via patch-pairs leaning based methods has been wildly used in the past several years. Some position-patch based face hallucination methods have been proposed to improve the representation power of image patch and obtain the optimal regressive weighted vector. The rationale behind the position-patch based face hallucination is the fact that human face is always highly structured and consequently positioned and it plays an increasingly important role in the reconstruction. However, in the existing position-patch based methods,the probe image patch is usually represented as a linear combination of the corresponding patches of some training images, and the reconstruction residual is usually measured using the vector norm such as 1-norm and 2-norm.Since the vector norms neglect two-dimensional structures inside the residual, the final reconstruction performance is not very satisfactory. To cope with this problem, we present a weighted nuclear-norm constrained sparse coding(WNCSC) model for position-patch based face hallucination. In addition, an efficient algorithm for the WNCSC is developed using the alternating direction method of multipliers(ADMM) and the method of augmented Lagrange multipliers(ALM). The advantages of the proposed model are twofold: in order to fully make use of low-rank structure information of the reconstruction residual, the weighted nuclear norm is applied to measure the residual matrix, which is able to alleviate the bias between input patches and training data, and it is more robust than the Euclidean distance(2-norm); the more flexible selection method for rank components can determine the optimal combination weights and adaptively choose the relevant and nearest hallucinated neighbors. Finally, experimental results prove that the proposed method outperforms the related state-of-the-art methods in both quantitative and visual comparisons.展开更多
In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minim...In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.展开更多
本文提出了一个超声图像复原模型,该模型融合了加权核范数最小化和数据保真度。加权核范数最小化能够自适应处理奇异值以保留图像细节,数据保真度则增强了图像复原效果。本研究采用交替方向乘子法(Alternating Direction Method of Mult...本文提出了一个超声图像复原模型,该模型融合了加权核范数最小化和数据保真度。加权核范数最小化能够自适应处理奇异值以保留图像细节,数据保真度则增强了图像复原效果。本研究采用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)高效求解,并通过实验结果验证了该方法的优越性。展开更多
基金supported by the National Natural Science Foundation of China(6140130861572063)+7 种基金the Natural Science Foundation of Hebei Province(F2016201142F2016201187)the Natural Social Foundation of Hebei Province(HB15TQ015)the Science Research Project of Hebei Province(QN2016085ZC2016040)the Science and Technology Support Project of Hebei Province(15210409)the Natural Science Foundation of Hebei University(2014-303)the National Comprehensive Ability Promotion Project of Western and Central China
文摘As synthetic aperture radar（SAR） has been widely used nearly in every field, SAR image de-noising became a very important research field. A new SAR image de-noising method based on texture strength and weighted nuclear norm minimization（WNNM） is proposed. To implement blind de-noising, the accurate estimation of noise variance is very important. So far, it is still a challenge to estimate SAR image noise level accurately because of the rich texture. Principal component analysis（PCA） and the low rank patches selected by image texture strength are used to estimate the noise level. With the help of noise level, WNNM can be expected to SAR image de-noising. Experimental results show that the proposed method outperforms many excellent de-noising algorithms such as Bayes least squares-Gaussian scale mixtures（BLS-GSM） method, non-local means（NLM） filtering in terms of both quantitative measure and visual perception quality.
基金This work is supported by the National Natural Science Foundation of China nos.11971215 and 11571156,MOE-LCSMSchool of Mathematics and Statistics,Hunan Normal University,Changsha,Hunan 410081,China.
文摘Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.
基金financially supported by the National Nautral Science Foundation of China(No.61703206)
文摘Non-convex methods play a critical role in low-rank tensor completion for their approximation to tensor rank is tighter than that of convex methods.But they usually cost much more time for calculating singular values of large tensors.In this paper,we propose a double transformed tubal nuclear norm(DTTNN)to replace the rank norm penalty in low rank tensor completion(LRTC)tasks.DTTNN turns the original non-convex penalty of a large tensor into two convex penalties of much smaller tensors,and it is shown to be an equivalent transformation.Therefore,DTTNN could take advantage of non-convex envelopes while saving time.Experimental results on color image and video inpainting tasks verify the effectiveness of DTTNN compared with state-of-the-art methods.
基金the National Natural Science Foundation of China(Nos.61702269,61171165,11431015 and 61571230)the Natural Science Foundation of Jiangsu Province(No.BK20171074)+1 种基金the Natural Science Foundation of Guangxi Province(No.2014GXNSFAA118360)the National Scientific Equipment Developing Project of China(No.2012YQ050250)
文摘Face hallucination via patch-pairs leaning based methods has been wildly used in the past several years. Some position-patch based face hallucination methods have been proposed to improve the representation power of image patch and obtain the optimal regressive weighted vector. The rationale behind the position-patch based face hallucination is the fact that human face is always highly structured and consequently positioned and it plays an increasingly important role in the reconstruction. However, in the existing position-patch based methods,the probe image patch is usually represented as a linear combination of the corresponding patches of some training images, and the reconstruction residual is usually measured using the vector norm such as 1-norm and 2-norm.Since the vector norms neglect two-dimensional structures inside the residual, the final reconstruction performance is not very satisfactory. To cope with this problem, we present a weighted nuclear-norm constrained sparse coding(WNCSC) model for position-patch based face hallucination. In addition, an efficient algorithm for the WNCSC is developed using the alternating direction method of multipliers(ADMM) and the method of augmented Lagrange multipliers(ALM). The advantages of the proposed model are twofold: in order to fully make use of low-rank structure information of the reconstruction residual, the weighted nuclear norm is applied to measure the residual matrix, which is able to alleviate the bias between input patches and training data, and it is more robust than the Euclidean distance(2-norm); the more flexible selection method for rank components can determine the optimal combination weights and adaptively choose the relevant and nearest hallucinated neighbors. Finally, experimental results prove that the proposed method outperforms the related state-of-the-art methods in both quantitative and visual comparisons.
基金supported by the National Natural Science Foundation of China under grants U21A20455,61972265,11871348 and 11701388by the Natural Science Foundation of Guangdong Province of China under grant 2020B1515310008by the Educational Commission of Guangdong Province of China under grant 2019KZDZX1007.
文摘In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.
文摘本文提出了一个超声图像复原模型,该模型融合了加权核范数最小化和数据保真度。加权核范数最小化能够自适应处理奇异值以保留图像细节,数据保真度则增强了图像复原效果。本研究采用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)高效求解,并通过实验结果验证了该方法的优越性。
