In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal fu...In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal function such that the closed form solutions of the subproblem can be easily derived.In the subproblem, we apply a variable stepsize, that is like Barzilai-Borwein stepsize, to accelerate the algorithm. Numerical results with parallel magnetic resonance imaging demonstrate the efficiency of the proposed algorithm.展开更多
Recently, a number of large molybdenum (-copper) deposits have been discovered successively in the Laba area, Shangri-La county, northwestern Yunnan province. The investigation confirmed that there is a superlarge por...Recently, a number of large molybdenum (-copper) deposits have been discovered successively in the Laba area, Shangri-La county, northwestern Yunnan province. The investigation confirmed that there is a superlarge porphyry-skarn hydrothermal vein type molybdenum-polymetallic- metallogenic system with the total prediction reservoir of more than 150 mt molybdenum. The porphyry intrusions contributed to the mineralization closely, the superficial little vein molybdenum (-copper, lead, silver) ore-bodies are usually located in faults and fractures, and the deep porphyry type ore-bodies occurred in the granodiorite porphyries, the skarn type ore-bodies occurred in the contact zone intrused into Triassic limestone or Permian basalts. Laba ore block is a new exploration area with great prospecting potential. In order to reduce the target area and guide the further exploration work, the magnetic method measurement about 3.3 square kilometres was carried out in the ore field. This paper presents an application of analyzing the horizontal and vertical derivative, using Fast Fourier Transform (FFT) filter (FFT high-pass, low-pass, cosine roll-off, suscepbility), calculated spectra frequency energy to predict the depth and intensity of the apparent remanence magnetization of source (Hilbert). The calculated results and magnetic anomalous show that the remanence anomaly is caused by the intrusions into the Triassic limestone and Permian basalts with small anomalies, and the depth of located source is not great. We have identified a number of positions to the three drilled well, the drilled result specify interpretation with very high accuracy. The magnetic method is helpful to identify porphyry mineralization, and judge the shape and depth of the concealed ore-bearing intrusive bodies under the similar geological condition.展开更多
In recent years,utilizing the low-rank prior information to construct a signal from a small amount of measures has attracted much attention.In this paper,a generalized nonconvex low-rank(GNLR) algorithm for magnetic r...In recent years,utilizing the low-rank prior information to construct a signal from a small amount of measures has attracted much attention.In this paper,a generalized nonconvex low-rank(GNLR) algorithm for magnetic resonance imaging(MRI)reconstruction is proposed,which reconstructs the image from highly under-sampled k-space data.In the algorithm,the nonconvex surrogate function replacing the conventional nuclear norm is utilized to enhance the low-rank property inherent in the reconstructed image.An alternative direction multiplier method(ADMM) is applied to solving the resulting non-convex model.Extensive experimental results have demonstrated that the proposed method can consistently recover MRIs efficiently,and outperforms the current state-of-the-art approaches in terms of higher peak signal-to-noise ratio(PSNR) and lower high-frequency error norm(HFEN) values.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
In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the...In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p <...In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.展开更多
为了实现快速成像,磁共振指纹(Magnetic Resonance Fingerprinting,MRF)技术通常使用非笛卡尔稀疏采样模板对K空间进行高度欠采样,从而获得稀疏K空间信号.然而,从稀疏的K空间信号重建像空间数据是一个病态不适定问题,重建出的MRF像空间...为了实现快速成像,磁共振指纹(Magnetic Resonance Fingerprinting,MRF)技术通常使用非笛卡尔稀疏采样模板对K空间进行高度欠采样,从而获得稀疏K空间信号.然而,从稀疏的K空间信号重建像空间数据是一个病态不适定问题,重建出的MRF像空间数据存在大量的混叠伪影,直接影响到组织生理参数的重建准确度.为此需要将各种先验知识引入重建模型之中,以缓解MRF重建问题的不适定性.针对上述问题,本文提出一种融合局部低秩先验与Bloch流形约束的MRF重建模型,并使用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解模型中的非凸MRF重建问题.本文算法在引入MRF像空间数据的局部低秩先验的同时,使用预先构建的字典为重建指纹提供流形约束.一方面通过空域局部低秩约束有效抑制混叠伪影的产生,另一方面利用字典先验避免指纹的时域流形特征在迭代重建过程中丢失.仿真实验结果表明,相较于引入了全局低秩先验与Bloch流形约束的其他同类算法,本文算法可以提供更高的组织参数重建准确度.展开更多
A 3-D impedance method has been introduced to compute the electric currents induced in a human body exposed to extremely low-frequency electromagnetic field. The 3-D impedance method has been deduced from Maxwell equa...A 3-D impedance method has been introduced to compute the electric currents induced in a human body exposed to extremely low-frequency electromagnetic field. The 3-D impedance method has been deduced from Maxwell equations and is put into the computation and simulation effectively to the visible human body model, which has 196×114×626 cells and more than 40 types of tissues. As the result, two representative cases are investigated. One is exposure of the human body to 100 μT (1 000 mG), the limit recommended by the International Commission on Non-Ionizing Radiation Protection for the public and the other one is the exposure of human body to 0.4 laT (4 mG), the level at which a statistical link appears with a doubled risk of development of childhood leukaemia. The distribution of induced current density can be obtained and the maximum of induced current are found to be 16 mA/m^2 and 0.07 mA/m^2.展开更多
基金supported in part by the National Natural Science Foundation of China(11361018,11461015)Guangxi Natural Science Foundation(2014GXNSFFA118001)+3 种基金Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112,YQ16112)Guilin Science and Technology Project(20140127-2)the Innovation Project of Guangxi Graduate Education and Innovation Project of GUET Graduate Education(YJCXB201502)Guangxi Key Laboratory of Cryptography and Information Security(GCIS201624)
文摘In this study, we propose a linearized proximal alternating direction method with variable stepsize for solving total variation image reconstruction problems. Our method uses a linearized technique and the proximal function such that the closed form solutions of the subproblem can be easily derived.In the subproblem, we apply a variable stepsize, that is like Barzilai-Borwein stepsize, to accelerate the algorithm. Numerical results with parallel magnetic resonance imaging demonstrate the efficiency of the proposed algorithm.
文摘Recently, a number of large molybdenum (-copper) deposits have been discovered successively in the Laba area, Shangri-La county, northwestern Yunnan province. The investigation confirmed that there is a superlarge porphyry-skarn hydrothermal vein type molybdenum-polymetallic- metallogenic system with the total prediction reservoir of more than 150 mt molybdenum. The porphyry intrusions contributed to the mineralization closely, the superficial little vein molybdenum (-copper, lead, silver) ore-bodies are usually located in faults and fractures, and the deep porphyry type ore-bodies occurred in the granodiorite porphyries, the skarn type ore-bodies occurred in the contact zone intrused into Triassic limestone or Permian basalts. Laba ore block is a new exploration area with great prospecting potential. In order to reduce the target area and guide the further exploration work, the magnetic method measurement about 3.3 square kilometres was carried out in the ore field. This paper presents an application of analyzing the horizontal and vertical derivative, using Fast Fourier Transform (FFT) filter (FFT high-pass, low-pass, cosine roll-off, suscepbility), calculated spectra frequency energy to predict the depth and intensity of the apparent remanence magnetization of source (Hilbert). The calculated results and magnetic anomalous show that the remanence anomaly is caused by the intrusions into the Triassic limestone and Permian basalts with small anomalies, and the depth of located source is not great. We have identified a number of positions to the three drilled well, the drilled result specify interpretation with very high accuracy. The magnetic method is helpful to identify porphyry mineralization, and judge the shape and depth of the concealed ore-bearing intrusive bodies under the similar geological condition.
基金National Natural Science Foundations of China(Nos.61362001,61365013,51165033)the Science and Technology Department of Jiangxi Province of China(Nos.20132BAB211030,20122BAB211015)+1 种基金the Jiangxi Advanced Projects for Postdoctoral Research Funds,China(o.2014KY02)the Innovation Special Fund Project of Nanchang University,China(o.cx2015136)
文摘In recent years,utilizing the low-rank prior information to construct a signal from a small amount of measures has attracted much attention.In this paper,a generalized nonconvex low-rank(GNLR) algorithm for magnetic resonance imaging(MRI)reconstruction is proposed,which reconstructs the image from highly under-sampled k-space data.In the algorithm,the nonconvex surrogate function replacing the conventional nuclear norm is utilized to enhance the low-rank property inherent in the reconstructed image.An alternative direction multiplier method(ADMM) is applied to solving the resulting non-convex model.Extensive experimental results have demonstrated that the proposed method can consistently recover MRIs efficiently,and outperforms the current state-of-the-art approaches in terms of higher peak signal-to-noise ratio(PSNR) and lower high-frequency error norm(HFEN) values.
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.
基金Supported by the National Natural Science Foundation of China(No.61261010No.61362001+7 种基金No.61365013No.61262084No.51165033)Technology Foundation of Department of Education in Jiangxi Province(GJJ13061GJJ14196)Young Scientists Training Plan of Jiangxi Province(No.20133ACB21007No.20142BCB23001)National Post-Doctoral Research Fund(No.2014M551867)and Jiangxi Advanced Project for Post-Doctoral Research Fund(No.2014KY02)
文摘In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
基金the National Natural Science Foundation of China(Nos.6136200161365013 and 51165033)+3 种基金the Natural Science Foundation of Jiangxi Province(Nos.20132BAB211030 and 20122BAB211015)the Technology Foundation of Department of Education in Jiangxi Province(Nos.GJJ 13061 and GJJ14196)the National Postdoctoral Research Funds(No.2014M551867)the Jiangxi Advanced Projects for Postdoctoral Research Funds(No.2014KY02)
文摘In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.
文摘为了实现快速成像,磁共振指纹(Magnetic Resonance Fingerprinting,MRF)技术通常使用非笛卡尔稀疏采样模板对K空间进行高度欠采样,从而获得稀疏K空间信号.然而,从稀疏的K空间信号重建像空间数据是一个病态不适定问题,重建出的MRF像空间数据存在大量的混叠伪影,直接影响到组织生理参数的重建准确度.为此需要将各种先验知识引入重建模型之中,以缓解MRF重建问题的不适定性.针对上述问题,本文提出一种融合局部低秩先验与Bloch流形约束的MRF重建模型,并使用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)求解模型中的非凸MRF重建问题.本文算法在引入MRF像空间数据的局部低秩先验的同时,使用预先构建的字典为重建指纹提供流形约束.一方面通过空域局部低秩约束有效抑制混叠伪影的产生,另一方面利用字典先验避免指纹的时域流形特征在迭代重建过程中丢失.仿真实验结果表明,相较于引入了全局低秩先验与Bloch流形约束的其他同类算法,本文算法可以提供更高的组织参数重建准确度.
基金This work is supported by the National Natural Science Foundation of China (60671055, 60331010);Innovation Foundation from Beijing University of Posts and Telecommunications.
文摘A 3-D impedance method has been introduced to compute the electric currents induced in a human body exposed to extremely low-frequency electromagnetic field. The 3-D impedance method has been deduced from Maxwell equations and is put into the computation and simulation effectively to the visible human body model, which has 196×114×626 cells and more than 40 types of tissues. As the result, two representative cases are investigated. One is exposure of the human body to 100 μT (1 000 mG), the limit recommended by the International Commission on Non-Ionizing Radiation Protection for the public and the other one is the exposure of human body to 0.4 laT (4 mG), the level at which a statistical link appears with a doubled risk of development of childhood leukaemia. The distribution of induced current density can be obtained and the maximum of induced current are found to be 16 mA/m^2 and 0.07 mA/m^2.