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
The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis(ICA).However,it is hard to take both stability and speed into consideration in processing functi...The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis(ICA).However,it is hard to take both stability and speed into consideration in processing functional magnetic resonance imaging(fMRI)data.In this paper,an optimization model for ICA is presented and an improved fixed-point algorithm based on the model is proposed.In the new algorithms a small step size is added to increase the stability.In order to accelerate the convergence,an improvement on Newton method is made,which makes cubic convergence for the new algorithm.Applying the algorithm and two other algorithms to invivo fMRI data,the results show that the new algorithm separates independent components stably,which has faster convergence speed and less computation than the other two algorithms.The algorithm has obvious advantage in processing fMRI signal with huge data.展开更多
This paper proves the error reduction property （saturation property）, convergence and optimality of an adaptive mixed finite element method （AMFEM） for the Poisson equation. In each step of AMFEM, the local refine...This paper proves the error reduction property （saturation property）, convergence and optimality of an adaptive mixed finite element method （AMFEM） for the Poisson equation. In each step of AMFEM, the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations, depending only on the marking strategy, under some restriction of refinement. The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe （2006） and the quasi-orthogonality estimate proved by Chen, Holst, and Xu （2009）. Numerical experiments fully confirm the theoretical analysis.展开更多
This paper decomposes the economic growth of the Yangtze River Delta into physical capital accumulation, improved efficiency, technological progress, and human capital input based on the non-parametric DEA method. It ...This paper decomposes the economic growth of the Yangtze River Delta into physical capital accumulation, improved efficiency, technological progress, and human capital input based on the non-parametric DEA method. It then examines the convergence effects of these four factors and the growth rate of the Delta using spatial statistic and econometric techniques and employing the absolute convergence equation. Our empirical findings show that the economic contribution of physical capital drives the real economic growth of the Delta＇s counties, cities and districts. Regional economic growth exhibits a significant spatial dependence which has had a marked effect on trends in economic growth. The neo- classical economic growth factor, physical capital accumulation, is the only factor involved in narrowing the gap among different parts of the Delta region and has driven the trend of economic convergence. Other new economic growth factors such as human capital, improved efficiency and technological progress have resulted in divergence in the Delta＇s economic growth and have had a profound impact on the economic disparities among different parts of the Delta region.展开更多
This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors de...This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.展开更多
One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient fun...One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.展开更多
Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression,signal processing and statistics,etc.For Calder′on-Zygmund operators T,it is interestin...Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression,signal processing and statistics,etc.For Calder′on-Zygmund operators T,it is interesting to construct estimator of T f,based on wavelet shrinkage estimator of f.With the help of a representation of operators on wavelets,due to Beylkin et al.,an estimator of T f is presented in this paper.The almost everywhere convergence and norm convergence of the proposed estimators are established.展开更多
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.
文摘The fixed-point algorithm and infomax algorithm are two of the most popular algorithms in independent component analysis(ICA).However,it is hard to take both stability and speed into consideration in processing functional magnetic resonance imaging(fMRI)data.In this paper,an optimization model for ICA is presented and an improved fixed-point algorithm based on the model is proposed.In the new algorithms a small step size is added to increase the stability.In order to accelerate the convergence,an improvement on Newton method is made,which makes cubic convergence for the new algorithm.Applying the algorithm and two other algorithms to invivo fMRI data,the results show that the new algorithm separates independent components stably,which has faster convergence speed and less computation than the other two algorithms.The algorithm has obvious advantage in processing fMRI signal with huge data.
基金supported in part by the Natural Science Foundation of China under Grant No.10771150the National Basic Research Program of China under Grant No.2005CB321701the Natural Science Foundation of Chongqing City under Grant No.CSTC,2010BB8270
文摘This paper proves the error reduction property （saturation property）, convergence and optimality of an adaptive mixed finite element method （AMFEM） for the Poisson equation. In each step of AMFEM, the local refinement is performed basing on simple either edge-oriented residuals or edge-oriented data oscillations, depending only on the marking strategy, under some restriction of refinement. The main tools used here are the strict discrete local efficiency property given by Carstensen and Hoppe （2006） and the quasi-orthogonality estimate proved by Chen, Holst, and Xu （2009）. Numerical experiments fully confirm the theoretical analysis.
基金This project is funded by the National Natural Science Foundation of China(No.70803030)the Shuguang Project funded by the Shanghai Municipal Education Commission and the Shanghai Education Development Foundation(No.11SG36)
文摘This paper decomposes the economic growth of the Yangtze River Delta into physical capital accumulation, improved efficiency, technological progress, and human capital input based on the non-parametric DEA method. It then examines the convergence effects of these four factors and the growth rate of the Delta using spatial statistic and econometric techniques and employing the absolute convergence equation. Our empirical findings show that the economic contribution of physical capital drives the real economic growth of the Delta＇s counties, cities and districts. Regional economic growth exhibits a significant spatial dependence which has had a marked effect on trends in economic growth. The neo- classical economic growth factor, physical capital accumulation, is the only factor involved in narrowing the gap among different parts of the Delta region and has driven the trend of economic convergence. Other new economic growth factors such as human capital, improved efficiency and technological progress have resulted in divergence in the Delta＇s economic growth and have had a profound impact on the economic disparities among different parts of the Delta region.
基金supported by the National Natural Science Foundation of China(No.11271286)the Specialized Research Fund for the Doctor Program of Higher Education of China(No.20120072110007)a grant from the Natural Sciences and Engineering Research Council of Canada
文摘This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.
基金supported by National Natural Science Foundation of China under Grant No.1117112the Fund of Shanxi Datong University under Grant No.2010K4+1 种基金the Doctoral Fund of Ministry of Education of China under Grant No.20090076110001National Statistical Science Research Major Program of China under Grant No.2011LZ051
文摘One important model in handling the multivariate data is the varying-coefficient partially linear regression model. In this paper, the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not. It is showed that the normalized proposed test follows asymptotically x2-distribution and the Wilks phenomenon under the null hypothesis, and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing. Some simulation studies illustrate that the test works well.
基金supported by National Natural Science Foundation of China(Grant Nos.11171014 and 91130009)National Basic Research Program of China(Grant No.973-2010CB-731900)
文摘Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression,signal processing and statistics,etc.For Calder′on-Zygmund operators T,it is interesting to construct estimator of T f,based on wavelet shrinkage estimator of f.With the help of a representation of operators on wavelets,due to Beylkin et al.,an estimator of T f is presented in this paper.The almost everywhere convergence and norm convergence of the proposed estimators are established.
