To improve the accuracy and effectiveness of continuous-time(CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization(NNM) with the generalized Poisson moment fun...To improve the accuracy and effectiveness of continuous-time(CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization(NNM) with the generalized Poisson moment functional(GPMF)based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method(SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers(ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods.展开更多
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
The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant...The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant( LTI) system and a static nonlinear function( the linear part is followed by the nonlinear part). The nonlinear function is approximated by the pseudospectral basis functions, which have a better performance than Hinge functions and Radial Basis functions. After the approximation on the nonlinear function, the CT Hammerstein system has been transformed into a multiple-input single-output( MISO) linear model system with the differential pre-filters. However, the coefficients of static nonlinearity and the numerators of the linear transfer function are coupled together to challenge the parameters identification of the Hammerstein system. This problem is solved by replacing the one-rank constraint of the regularization optimization with the nuclear norm convex relaxation. Finally, a numerical example is given to verify the accuracy and the efficiency of the method.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
阵元失效下多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达虚拟阵列协方差矩阵出现大批整行整列元素缺失,破坏原有内在完整结构,导致波达方向(Direction of Arrival,DOA)估计性能下降。为此,提出一种联合核范数和SCAD(Smoothly...阵元失效下多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达虚拟阵列协方差矩阵出现大批整行整列元素缺失,破坏原有内在完整结构,导致波达方向(Direction of Arrival,DOA)估计性能下降。为此,提出一种联合核范数和SCAD(Smoothly Clipped Absolute Deviation)惩罚的完整协方差矩阵重构方法,以利于阵元失效下MIMO雷达DOA的有效估计。首先对待恢复的协方差矩阵建立核范数和SCAD惩罚双先验约束模型,并利用等正弦空间稀疏化方式划分粗网格空间,在可容忍的模型误差内能大大降低运算复杂度;然后利用ALM-ADMM(Augmented Lagrange Multipliers-Alternating Direction Method of Multipliers)算法对双先验约束模型进行求解,从而恢复协方差矩阵中大量整行整列的缺失数据;最后通过RD-ESPRIT(Reduced Dimensional ESPRIT)算法进行目标DOA估计。仿真结果验证该方法能快速恢复虚拟协方差矩阵中的缺失数据,从而有效提高阵元失效下MIMO雷达的DOA估计性能。展开更多
文摘To improve the accuracy and effectiveness of continuous-time(CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization(NNM) with the generalized Poisson moment functional(GPMF)based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method(SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers(ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods.
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.
文摘The nuclear norm convex relaxation method is proposed to force the rank constraint in the identification of the continuous-time( CT) Hammerstein system. The CT Hammerstein system is composed of a linear time invariant( LTI) system and a static nonlinear function( the linear part is followed by the nonlinear part). The nonlinear function is approximated by the pseudospectral basis functions, which have a better performance than Hinge functions and Radial Basis functions. After the approximation on the nonlinear function, the CT Hammerstein system has been transformed into a multiple-input single-output( MISO) linear model system with the differential pre-filters. However, the coefficients of static nonlinearity and the numerators of the linear transfer function are coupled together to challenge the parameters identification of the Hammerstein system. This problem is solved by replacing the one-rank constraint of the regularization optimization with the nuclear norm convex relaxation. Finally, a numerical example is given to verify the accuracy and the efficiency of the method.
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.
文摘阵元失效下多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达虚拟阵列协方差矩阵出现大批整行整列元素缺失,破坏原有内在完整结构,导致波达方向(Direction of Arrival,DOA)估计性能下降。为此,提出一种联合核范数和SCAD(Smoothly Clipped Absolute Deviation)惩罚的完整协方差矩阵重构方法,以利于阵元失效下MIMO雷达DOA的有效估计。首先对待恢复的协方差矩阵建立核范数和SCAD惩罚双先验约束模型,并利用等正弦空间稀疏化方式划分粗网格空间,在可容忍的模型误差内能大大降低运算复杂度;然后利用ALM-ADMM(Augmented Lagrange Multipliers-Alternating Direction Method of Multipliers)算法对双先验约束模型进行求解,从而恢复协方差矩阵中大量整行整列的缺失数据;最后通过RD-ESPRIT(Reduced Dimensional ESPRIT)算法进行目标DOA估计。仿真结果验证该方法能快速恢复虚拟协方差矩阵中的缺失数据,从而有效提高阵元失效下MIMO雷达的DOA估计性能。