In this paper, we modify the Bregman APG<sub>s</sub> (BAPG<sub>s</sub>) method proposed in (Wang, L, et al.) for solving the support vector machine problem with truncated loss (HTPSVM) given in...In this paper, we modify the Bregman APG<sub>s</sub> (BAPG<sub>s</sub>) method proposed in (Wang, L, et al.) for solving the support vector machine problem with truncated loss (HTPSVM) given in (Zhu, W, et al.), we also add an adaptive parameter selection technique based on (Ren, K, et al.). In each iteration, we use the linear approximation method to get the explicit solution of the subproblem and set a function to apply the Bregman distance. Finally, numerical experiments are performed to verify the efficiency of BAPG<sub>s</sub>.展开更多
In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multiplie...In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multipliers (ADMM), is employed to solve such problems typically, which still requires the assumption of the gradient Lipschitz continuity condition on the objective function to ensure overall convergence from the current knowledge. However, many practical applications do not adhere to the conditions of smoothness. In this study, we justify the convergence of variant Bregman ADMM for the problem with coupling terms to circumvent the issue of the global Lipschitz continuity of the gradient. We demonstrate that the iterative sequence generated by our approach converges to a critical point of the issue when the corresponding function fulfills the Kurdyka-Lojasiewicz inequality and certain assumptions apply. In addition, we illustrate the convergence rate of the algorithm.展开更多
We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteratio...We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.展开更多
To improve the anti-noise performance of the time-domain Bregman iterative algorithm,an adaptive frequency-domain Bregman sparse-spike deconvolution algorithm is proposed.By solving the Bregman algorithm in the freque...To improve the anti-noise performance of the time-domain Bregman iterative algorithm,an adaptive frequency-domain Bregman sparse-spike deconvolution algorithm is proposed.By solving the Bregman algorithm in the frequency domain,the influence of Gaussian as well as outlier noise on the convergence of the algorithm is effectively avoided.In other words,the proposed algorithm avoids data noise effects by implementing the calculations in the frequency domain.Moreover,the computational efficiency is greatly improved compared with the conventional method.Generalized cross validation is introduced in the solving process to optimize the regularization parameter and thus the algorithm is equipped with strong self-adaptation.Different theoretical models are built and solved using the algorithms in both time and frequency domains.Finally,the proposed and the conventional methods are both used to process actual seismic data.The comparison of the results confirms the superiority of the proposed algorithm due to its noise resistance and self-adaptation capability.展开更多
In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, ...In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent highprecision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model and fi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data.展开更多
The classical TV (Total Variation) model has been applied to gray texture image denoising and inpainting previously based on the non local operators, but such model can not be directly used to color texture image inpa...The classical TV (Total Variation) model has been applied to gray texture image denoising and inpainting previously based on the non local operators, but such model can not be directly used to color texture image inpainting due to coupling of different image layers in color images. In order to solve the inpainting problem for color texture images effectively, we propose a non local CTV (Color Total Variation) model. Technically, the proposed model is an extension of local TV model for gray images but we take account of the coupling of different layers in color images and make use of concepts of the non-local operators. As the coupling of different layers for color images in the proposed model will in-crease computational complexity, we also design a fast Split Bregman algorithm. Finally, some numerical experiments are conducted to validate the performance of the proposed model and its algorithm.展开更多
As a complement to X-ray computed tomography(CT),neutron tomography has been extensively used in nuclear engineer-ing,materials science,cultural heritage,and industrial applications.Reconstruction of the attenuation m...As a complement to X-ray computed tomography(CT),neutron tomography has been extensively used in nuclear engineer-ing,materials science,cultural heritage,and industrial applications.Reconstruction of the attenuation matrix for neutron tomography with a traditional analytical algorithm requires hundreds of projection views in the range of 0°to 180°and typically takes several hours to complete.Such a low time-resolved resolution degrades the quality of neutron imaging.Decreasing the number of projection acquisitions is an important approach to improve the time resolution of images;however,this requires efficient reconstruction algorithms.Therefore,sparse-view reconstruction algorithms in neutron tomography need to be investigated.In this study,we investigated the three-dimensional reconstruction algorithm for sparse-view neu-tron CT scans.To enhance the reconstructed image quality of neutron CT,we propose an algorithm that uses OS-SART to reconstruct images and a split Bregman to solve for the total variation(SBTV).A comparative analysis of the performances of each reconstruction algorithm was performed using simulated and actual experimental data.According to the analyzed results,OS-SART-SBTV is superior to the other algorithms in terms of denoising,suppressing artifacts,and preserving detailed structural information of images.展开更多
To improve the economic efficiency of urban integrated energy systems(UIESs)and mitigate day-ahead dispatch uncertainty,this paper presents an interconnected UIES and transmission system(TS)model based on distributed ...To improve the economic efficiency of urban integrated energy systems(UIESs)and mitigate day-ahead dispatch uncertainty,this paper presents an interconnected UIES and transmission system(TS)model based on distributed robust optimization.First,interconnections are established between a TS and multiple UIESs,as well as among different UIESs,each incorporating multiple energy forms.The Bregman alternating direction method with multipliers(BADMM)is then applied to multi-block problems,ensuring the privacy of each energy system operator(ESO).Second,robust optimization based on wind probability distribution information is implemented for each ESO to address dispatch uncertainty.The column and constraint generation(C&CG)algorithm is then employed to solve the robust model.Third,to tackle the convergence and practicability issues overlooked in the existing studies,an external C&CG with an internal BADMM and corresponding acceleration strategy is devised.Finally,numerical results demonstrate that the adoption of the proposed model and method for absorbing wind power and managing its uncertainty results in economic benefits.展开更多
In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Bana...In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions.展开更多
In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. ...In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.展开更多
In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in ...In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.展开更多
The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly ...The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.展开更多
As X-ray computed tomography （CT） is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this pur- pose, one may use the TV based methods or w...As X-ray computed tomography （CT） is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this pur- pose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the in- terior tomography scheme which only illuminates a region-of-interest （ROI）, one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three differ- ent parts： cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART＋TV methods in terms of preservation of sharp edges, mean structural similarity （SSIM）, contrast-to-noise ratio, relative error and correlation- s. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART^TV methods need more than 200 projections. Additionally, the proposed ro- bust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART＋TV methods.展开更多
The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) ...The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.展开更多
文摘In this paper, we modify the Bregman APG<sub>s</sub> (BAPG<sub>s</sub>) method proposed in (Wang, L, et al.) for solving the support vector machine problem with truncated loss (HTPSVM) given in (Zhu, W, et al.), we also add an adaptive parameter selection technique based on (Ren, K, et al.). In each iteration, we use the linear approximation method to get the explicit solution of the subproblem and set a function to apply the Bregman distance. Finally, numerical experiments are performed to verify the efficiency of BAPG<sub>s</sub>.
文摘In this paper, our focus lies on addressing a two-block linearly constrained nonseparable nonconvex optimization problem with coupling terms. The most classical algorithm, the alternating direction method of multipliers (ADMM), is employed to solve such problems typically, which still requires the assumption of the gradient Lipschitz continuity condition on the objective function to ensure overall convergence from the current knowledge. However, many practical applications do not adhere to the conditions of smoothness. In this study, we justify the convergence of variant Bregman ADMM for the problem with coupling terms to circumvent the issue of the global Lipschitz continuity of the gradient. We demonstrate that the iterative sequence generated by our approach converges to a critical point of the issue when the corresponding function fulfills the Kurdyka-Lojasiewicz inequality and certain assumptions apply. In addition, we illustrate the convergence rate of the algorithm.
基金Supported by Youth Foundation of Southwest University of Science and Technology (No.11zx3126)
文摘We propose a new algorithm for the total variation based on image denoising problem. The split Bregman method is used to convert an unconstrained minimization denoising problem to a linear system in the outer iteration. An algebraic multi-grid method is applied to solve the linear system in the inner iteration. Furthermore, Krylov subspace acceleration is adopted to improve convergence in the outer iteration. Numerical experiments demonstrate that this algorithm is efficient even for images with large signal-to-noise ratio.
基金supported by the National Natural Science Foundation of China(No.NSFC 41204101)Open Projects Fund of the State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(No.PLN201733)+1 种基金Youth Innovation Promotion Association of the Chinese Academy of Sciences(No.2015051)Open Projects Fund of the Natural Gas and Geology Key Laboratory of Sichuan Province(No.2015trqdz03)
文摘To improve the anti-noise performance of the time-domain Bregman iterative algorithm,an adaptive frequency-domain Bregman sparse-spike deconvolution algorithm is proposed.By solving the Bregman algorithm in the frequency domain,the influence of Gaussian as well as outlier noise on the convergence of the algorithm is effectively avoided.In other words,the proposed algorithm avoids data noise effects by implementing the calculations in the frequency domain.Moreover,the computational efficiency is greatly improved compared with the conventional method.Generalized cross validation is introduced in the solving process to optimize the regularization parameter and thus the algorithm is equipped with strong self-adaptation.Different theoretical models are built and solved using the algorithms in both time and frequency domains.Finally,the proposed and the conventional methods are both used to process actual seismic data.The comparison of the results confirms the superiority of the proposed algorithm due to its noise resistance and self-adaptation capability.
基金supported by the National Natural Science Foundation of China(Nos.41274119,41174080,and 41004041)the 863 Program of China(No.2012AA09A20103)
文摘In seismic prospecting, fi eld conditions and other factors hamper the recording of the complete seismic wavefi eld; thus, data interpolation is critical in seismic data processing. Especially, in complex conditions, prestack missing data affect the subsequent highprecision data processing workfl ow. Compressive sensing is an effective strategy for seismic data interpolation by optimally representing the complex seismic wavefi eld and using fast and accurate iterative algorithms. The seislet transform is a sparse multiscale transform well suited for representing the seismic wavefield, as it can effectively compress seismic events. Furthermore, the Bregman iterative algorithm is an efficient algorithm for sparse representation in compressive sensing. Seismic data interpolation methods can be developed by combining seismic dynamic prediction, image transform, and compressive sensing. In this study, we link seismic data interpolation and constrained optimization. We selected the OC-seislet sparse transform to represent complex wavefields and used the Bregman iteration method to solve the hybrid norm inverse problem under the compressed sensing framework. In addition, we used an H-curve method to choose the threshold parameter in the Bregman iteration method. Thus, we achieved fast and accurate reconstruction of the seismic wavefi eld. Model and fi eld data tests demonstrate that the Bregman iteration method based on the H-curve norm in the sparse transform domain can effectively reconstruct missing complex wavefi eld data.
文摘The classical TV (Total Variation) model has been applied to gray texture image denoising and inpainting previously based on the non local operators, but such model can not be directly used to color texture image inpainting due to coupling of different image layers in color images. In order to solve the inpainting problem for color texture images effectively, we propose a non local CTV (Color Total Variation) model. Technically, the proposed model is an extension of local TV model for gray images but we take account of the coupling of different layers in color images and make use of concepts of the non-local operators. As the coupling of different layers for color images in the proposed model will in-crease computational complexity, we also design a fast Split Bregman algorithm. Finally, some numerical experiments are conducted to validate the performance of the proposed model and its algorithm.
基金supported by the National Key Research and Development Program of China(No.2022YFB1902700)the National Natural Science Foundation of China(No.11875129)+3 种基金the Fund of the State Key Laboratory of Intense Pulsed Radiation Simulation and Effect(No.SKLIPR1810)the Fund of Innovation Center of Radiation Application(No.KFZC2020020402)the Fund of the State Key Laboratory of Nuclear Physics and Technology,Peking University(No.NPT2020KFY08)the Joint Innovation Fund of China National Uranium Co.,Ltd.,State Key Laboratory of Nuclear Resources and Environment,East China University of Technology(No.2022NRE-LH-02).
文摘As a complement to X-ray computed tomography(CT),neutron tomography has been extensively used in nuclear engineer-ing,materials science,cultural heritage,and industrial applications.Reconstruction of the attenuation matrix for neutron tomography with a traditional analytical algorithm requires hundreds of projection views in the range of 0°to 180°and typically takes several hours to complete.Such a low time-resolved resolution degrades the quality of neutron imaging.Decreasing the number of projection acquisitions is an important approach to improve the time resolution of images;however,this requires efficient reconstruction algorithms.Therefore,sparse-view reconstruction algorithms in neutron tomography need to be investigated.In this study,we investigated the three-dimensional reconstruction algorithm for sparse-view neu-tron CT scans.To enhance the reconstructed image quality of neutron CT,we propose an algorithm that uses OS-SART to reconstruct images and a split Bregman to solve for the total variation(SBTV).A comparative analysis of the performances of each reconstruction algorithm was performed using simulated and actual experimental data.According to the analyzed results,OS-SART-SBTV is superior to the other algorithms in terms of denoising,suppressing artifacts,and preserving detailed structural information of images.
基金supported by the Science and Technology Project of State Grid Corporation of China(No.5108-202299259A-1-0-ZB)。
文摘To improve the economic efficiency of urban integrated energy systems(UIESs)and mitigate day-ahead dispatch uncertainty,this paper presents an interconnected UIES and transmission system(TS)model based on distributed robust optimization.First,interconnections are established between a TS and multiple UIESs,as well as among different UIESs,each incorporating multiple energy forms.The Bregman alternating direction method with multipliers(BADMM)is then applied to multi-block problems,ensuring the privacy of each energy system operator(ESO).Second,robust optimization based on wind probability distribution information is implemented for each ESO to address dispatch uncertainty.The column and constraint generation(C&CG)algorithm is then employed to solve the robust model.Third,to tackle the convergence and practicability issues overlooked in the existing studies,an external C&CG with an internal BADMM and corresponding acceleration strategy is devised.Finally,numerical results demonstrate that the adoption of the proposed model and method for absorbing wind power and managing its uncertainty results in economic benefits.
基金supported by the Natural Science Foundation of Fujian Province(Grant No.2014J01008)
文摘In this paper, we propose a new hybrid iterative scheme for finding a common solution to a finite of equilibrium problems and fixed point of Bregman totally quasi- asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions.
基金supported by the Province Natural Science Foundation of China(2014J01008)
文摘In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.
文摘In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.
文摘The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.
文摘As X-ray computed tomography （CT） is widely used in diagnosis and radiotherapy, it is important to reduce the radiation dose as low as reasonably achievable. For this pur- pose, one may use the TV based methods or wavelet frame based methods to reconstruct high quality images from reduced number of projections. Furthermore, by using the in- terior tomography scheme which only illuminates a region-of-interest （ROI）, one can save more radiation dose. In this paper, a robust wavelet frame regularization based model is proposed for both global reconstruction and interior tomography. The model can help to reduce the errors caused by mismatch of the huge sparse projection matrix. A three-system decomposition scheme is applied to decompose the reconstructed images into three differ- ent parts： cartoon, artifacts and noise. Therefore, by discarding the estimated artifacts and noise parts, the reconstructed images can be obtained with less noise and artifacts. Similar to other frame based image restoration models, the model can be efficiently solved by the split Bregman algorithm. Numerical simulations show that the proposed model outperforms the FBP and SART＋TV methods in terms of preservation of sharp edges, mean structural similarity （SSIM）, contrast-to-noise ratio, relative error and correlation- s. For example, for real sheep lung reconstruction, the proposed method can reach the mean structural similarity as high as 0.75 using only 100 projections while the FBP and the SART^TV methods need more than 200 projections. Additionally, the proposed ro- bust method is applicable for interior and exterior tomography with better performance compared to the FBP and the SART＋TV methods.
基金National Natural Science Foundations of China(Nos.61362001,61102043,61262084)Technology Foundations of Department of Education of Jiangxi Province,China(Nos.GJJ12006,GJJ14196)Natural Science Foundations of Jiangxi Province,China(Nos.20132BAB211030,20122BAB211015)
文摘The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.
