A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is refo...A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.展开更多
Synthetic aperture radar(SAR) image despeckling has been an attractive problem in remote sensing.The main challenge is to suppress speckle while preserving edges and preventing unnatural artifacts(such as annoying art...Synthetic aperture radar(SAR) image despeckling has been an attractive problem in remote sensing.The main challenge is to suppress speckle while preserving edges and preventing unnatural artifacts(such as annoying artifacts in homogeneous regions and over-smoothed edges).To address these problems,this paper proposes a new variational model with a nonconvex nonsmooth Lp(0 <p<1) norm regularization.It incorporates Lp(0<p<1) norm regularization and I-divergence fidelity term.Due to the nonconvex nonsmooth property,the regularization can better recover neat edges and homogeneous regions.The Ⅰ-divergence fidelity term is used to suppress the multiplicative noise effectively.Moreover,based on variable-splitting and alternating direction method of multipliers(ADMM) method,an efficient algorithm is proposed for solving this model.Intensive experimental results demonstrate that nonconvex nonsmooth model is superior to other state-of-the-art approaches qualitatively and quantitatively.展开更多
Networked microgrids(NMGs)are critical in theaccommodation of distributed renewable energy.However,theexisting centralized state estimation(SE)cannot meet the demandsof NMGs in distributed energy management.The curren...Networked microgrids(NMGs)are critical in theaccommodation of distributed renewable energy.However,theexisting centralized state estimation(SE)cannot meet the demandsof NMGs in distributed energy management.The currentestimator is also not robust against bad data.This study introducesthe concepts of relative error to construct an improvedrobust SE(IRSE)optimization model with mixed-integer nonlinearprogramming(MINLP)that overcomes the disadvantage ofinaccurate results derived from different measurements whenthe same tolerance range is considered in the robust SE(RSE).To improve the computation efficiency of the IRSE optimizationmodel,the number of binary variables is reduced based on theprojection statistics and normalized residual methods,which effectivelyavoid the problem of slow convergence or divergenceof the algorithm caused by too many integer variables.Finally,an embedded consensus alternating direction of multiplier method(ADMM)distribution algorithm based on outer approximation(OA)is proposed to solve the IRSE optimization model.This algorithm can accurately detect bad data and obtain SE resultsthat communicate only the boundary coupling informationwith neighbors.Numerical tests show that the proposed algorithmeffectively detects bad data,obtains more accurate SE results,and ensures the protection of private information in all microgrids.展开更多
Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,...Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,the Grunwald–Letnikov fractional-order derivative is usually used,where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator.In this paper,a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation(tFoTV)model is proposed for image restoration.Hopefully,first any boundary condition can be used in the numerical experiments.Second,the accuracy of the reconstructed images by the tFoTV model can be improved.The alternating directional method of multiplier is applied to solve the tFoTV model.Its convergence is also analyzed briefly.In the numerical experiments,we apply the tFoTV model to recover images that are corrupted by blur and noise.The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio(PSNR)than the full fractional-order variation and total variation models.From the numerical results,we can also see that the tFoTV model is comparable with the total generalized variation(TGV)model in accuracy.In addition,we can roughly fix a fractional order according to the structure of the image,and therefore,there is only one parameter left to determine in the tFoTV model,while there are always two parameters to be fixed in TGV model.展开更多
基金The Scientific Research Foundation of Nanjing University of Posts and Telecommunications(No.NY210049)
文摘A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.
基金Supported by the National Natural Science Foundation of China(No.41971356,41701446)the National Key Research and Development Program of China(No.2018YFB0505500)the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation,Ministry of Natural Resources(No.KF-2020-05-011)。
文摘Synthetic aperture radar(SAR) image despeckling has been an attractive problem in remote sensing.The main challenge is to suppress speckle while preserving edges and preventing unnatural artifacts(such as annoying artifacts in homogeneous regions and over-smoothed edges).To address these problems,this paper proposes a new variational model with a nonconvex nonsmooth Lp(0 <p<1) norm regularization.It incorporates Lp(0<p<1) norm regularization and I-divergence fidelity term.Due to the nonconvex nonsmooth property,the regularization can better recover neat edges and homogeneous regions.The Ⅰ-divergence fidelity term is used to suppress the multiplicative noise effectively.Moreover,based on variable-splitting and alternating direction method of multipliers(ADMM) method,an efficient algorithm is proposed for solving this model.Intensive experimental results demonstrate that nonconvex nonsmooth model is superior to other state-of-the-art approaches qualitatively and quantitatively.
基金supported by the National Natural Science Foundation of China(No.5217070269).
文摘Networked microgrids(NMGs)are critical in theaccommodation of distributed renewable energy.However,theexisting centralized state estimation(SE)cannot meet the demandsof NMGs in distributed energy management.The currentestimator is also not robust against bad data.This study introducesthe concepts of relative error to construct an improvedrobust SE(IRSE)optimization model with mixed-integer nonlinearprogramming(MINLP)that overcomes the disadvantage ofinaccurate results derived from different measurements whenthe same tolerance range is considered in the robust SE(RSE).To improve the computation efficiency of the IRSE optimizationmodel,the number of binary variables is reduced based on theprojection statistics and normalized residual methods,which effectivelyavoid the problem of slow convergence or divergenceof the algorithm caused by too many integer variables.Finally,an embedded consensus alternating direction of multiplier method(ADMM)distribution algorithm based on outer approximation(OA)is proposed to solve the IRSE optimization model.This algorithm can accurately detect bad data and obtain SE resultsthat communicate only the boundary coupling informationwith neighbors.Numerical tests show that the proposed algorithmeffectively detects bad data,obtains more accurate SE results,and ensures the protection of private information in all microgrids.
基金Raymond Honfu Chan’s research was supported in part by Hong Kong Research Grants Council(HKRGC)General Research Fund(No.CityU12500915,CityU14306316)HKRGC Collaborative Research Fund(No.C1007-15G)+2 种基金HKRGC Areas of Excellence(No.AoE/M-05/12)Hai-Xia Liang’s research was supported partly by the Natural Science Foundation of Jiangsu Province(No.BK20150373)partly by Xi’an Jiaotong-Liverpool University Research Enhancement Fund(No.17-01-08).
文摘Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed.In the existing works,the Grunwald–Letnikov fractional-order derivative is usually used,where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator.In this paper,a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation(tFoTV)model is proposed for image restoration.Hopefully,first any boundary condition can be used in the numerical experiments.Second,the accuracy of the reconstructed images by the tFoTV model can be improved.The alternating directional method of multiplier is applied to solve the tFoTV model.Its convergence is also analyzed briefly.In the numerical experiments,we apply the tFoTV model to recover images that are corrupted by blur and noise.The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio(PSNR)than the full fractional-order variation and total variation models.From the numerical results,we can also see that the tFoTV model is comparable with the total generalized variation(TGV)model in accuracy.In addition,we can roughly fix a fractional order according to the structure of the image,and therefore,there is only one parameter left to determine in the tFoTV model,while there are always two parameters to be fixed in TGV model.
