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
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
针对低信噪比情况下地震信号同相轴不易识别的问题,提出用C-WNNM方法来压制地震勘探资料中的随机噪声.给出了基于WNNM的低秩逼近理论,利用地震信号在时间和空间上具有一定的相似性这一特点来构建近似低秩矩阵,并且由CEEMD分解得到的IMF...针对低信噪比情况下地震信号同相轴不易识别的问题,提出用C-WNNM方法来压制地震勘探资料中的随机噪声.给出了基于WNNM的低秩逼近理论,利用地震信号在时间和空间上具有一定的相似性这一特点来构建近似低秩矩阵,并且由CEEMD分解得到的IMF1分量来近似估计局部噪声方差,从而获得更加精确的权值.经过迭代逼近得到最终去噪后的信号.对由雷克子波生成的模拟地震勘探资料进行C-WNNM滤波处理.结果表明,在地震数据存在强噪声的情况下,该方法能够有效压制随机噪声并且能够更好地保留有效信号,信噪比相比于原始WNNM算法提高了3 d B左右.展开更多
Low rank matrix recovery is a new topic drawing the attention of many researchers which addresses the problem of recovering an unknown low rank matrix from few linear measurements. The matrix Dantzig selector and the ...Low rank matrix recovery is a new topic drawing the attention of many researchers which addresses the problem of recovering an unknown low rank matrix from few linear measurements. The matrix Dantzig selector and the matrix Lasso are two important algorithms based on nuclear norm minimization. In this paper, we first prove some decay properties of restricted isometry constants, then we discuss the recovery errors of these two algorithms and give a new bound of restricted isometry constant to guarantee stable recovery, which improves the results of [11].展开更多
Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm ...Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm minimization. Those methods simultaneously minimize all the singular values, and thus the rank cannot be well approximated in practice. We extend the idea of truncated nuclear norm regularization(TNNR) to the robust PCA and consider truncated nuclear norm minimization(TNNM) instead of nuclear norm minimization(NNM). This method only minimizes the smallest N-r singular values to preserve the low-rank components, where N is the number of singular values and r is the matrix rank. Moreover, we propose an effective way to determine r via the shrinkage operator. Then we develop an effective iterative algorithm based on the alternating direction method to solve this optimization problem. Experimental results demonstrate the efficiency and accuracy of the TNNM method. Moreover, this method is much more robust in terms of the rank of the reconstructed matrix and the sparsity of the error.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。
文摘针对低信噪比情况下地震信号同相轴不易识别的问题,提出用C-WNNM方法来压制地震勘探资料中的随机噪声.给出了基于WNNM的低秩逼近理论,利用地震信号在时间和空间上具有一定的相似性这一特点来构建近似低秩矩阵,并且由CEEMD分解得到的IMF1分量来近似估计局部噪声方差,从而获得更加精确的权值.经过迭代逼近得到最终去噪后的信号.对由雷克子波生成的模拟地震勘探资料进行C-WNNM滤波处理.结果表明,在地震数据存在强噪声的情况下,该方法能够有效压制随机噪声并且能够更好地保留有效信号,信噪比相比于原始WNNM算法提高了3 d B左右.
基金Supported by the National Natural Science Foundation of China(No.11171299)
文摘Low rank matrix recovery is a new topic drawing the attention of many researchers which addresses the problem of recovering an unknown low rank matrix from few linear measurements. The matrix Dantzig selector and the matrix Lasso are two important algorithms based on nuclear norm minimization. In this paper, we first prove some decay properties of restricted isometry constants, then we discuss the recovery errors of these two algorithms and give a new bound of restricted isometry constant to guarantee stable recovery, which improves the results of [11].
基金the Doctoral Program of Higher Education of China(No.20120032110034)
文摘Robust principal component analysis(PCA) is widely used in many applications, such as image processing, data mining and bioinformatics. The existing methods for solving the robust PCA are mostly based on nuclear norm minimization. Those methods simultaneously minimize all the singular values, and thus the rank cannot be well approximated in practice. We extend the idea of truncated nuclear norm regularization(TNNR) to the robust PCA and consider truncated nuclear norm minimization(TNNM) instead of nuclear norm minimization(NNM). This method only minimizes the smallest N-r singular values to preserve the low-rank components, where N is the number of singular values and r is the matrix rank. Moreover, we propose an effective way to determine r via the shrinkage operator. Then we develop an effective iterative algorithm based on the alternating direction method to solve this optimization problem. Experimental results demonstrate the efficiency and accuracy of the TNNM method. Moreover, this method is much more robust in terms of the rank of the reconstructed matrix and the sparsity of the error.
