A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inne...A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
We study special functions related to Lotka-Volterra equations and negative Volterra equation intro-duced from zero curvature representations . At first we show the relationships between Lotka-Volterra equations intro...We study special functions related to Lotka-Volterra equations and negative Volterra equation intro-duced from zero curvature representations . At first we show the relationships between Lotka-Volterra equations introduced from zero curvature representations and symmetric orthogonal polynomials. Sec-ondarily, we describe the relationships between negative Volterra equations with a special solutions and cylinder functions.展开更多
The conformal transformations with respect to the metric defining the orthogonal Lie algebra o（n, C） give rise to a one-parameter （c） family of inhomogeneous first-order differential operator representations of th...The conformal transformations with respect to the metric defining the orthogonal Lie algebra o（n, C） give rise to a one-parameter （c） family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o（n ＋ 2, C）. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a^→∈ C^n, we prove that the space forms an irreducible o（n ＋ 2, C）-module for any c ∈ C if a^→ is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o（n＋2, C） on the polynomial algebra in n variables. Moreover, we prove that l forms an infinite-dimensional irreducible weight o（n ＋2, C）-module with finite-dimensional weight subspaces if c Z/2.展开更多
基金The National Natural Science Foundation of China (No.61362001,61102043,61262084,20132BAB211030,20122BAB211015)the Basic Research Program of Shenzhen(No.JC201104220219A)
文摘A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
文摘We study special functions related to Lotka-Volterra equations and negative Volterra equation intro-duced from zero curvature representations . At first we show the relationships between Lotka-Volterra equations introduced from zero curvature representations and symmetric orthogonal polynomials. Sec-ondarily, we describe the relationships between negative Volterra equations with a special solutions and cylinder functions.
基金supported by National Natural Science Foundation of China(Grant Nos.11171324 and 11321101)
文摘The conformal transformations with respect to the metric defining the orthogonal Lie algebra o（n, C） give rise to a one-parameter （c） family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o（n ＋ 2, C）. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a^→∈ C^n, we prove that the space forms an irreducible o（n ＋ 2, C）-module for any c ∈ C if a^→ is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o（n＋2, C） on the polynomial algebra in n variables. Moreover, we prove that l forms an infinite-dimensional irreducible weight o（n ＋2, C）-module with finite-dimensional weight subspaces if c Z/2.
