In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential...In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.展开更多
In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4...In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4）^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.展开更多
Sparse signal recovery problems are common in parameter estimation, image processing, pattern recognition, and so on. The problem of recovering a sparse signal representation from a signal dictionary might be classifi...Sparse signal recovery problems are common in parameter estimation, image processing, pattern recognition, and so on. The problem of recovering a sparse signal representation from a signal dictionary might be classified as a linear constraint l_0-quasinorm minimization problem, which is thought to be a Non-deterministic Polynomial-time（NP）-hard problem. Although several approximation methods have been developed to solve this problem via convex relaxation, researchers find the nonconvex methods to be more efficient in solving sparse recovery problems than convex methods. In this paper a nonconvex Exponential Metric Approximation（EMA）method is proposed to solve the sparse signal recovery problem. Our proposed EMA method aims to minimize a nonconvex negative exponential metric function to attain the sparse approximation and, with proper transformation,solve the problem via Difference Convex（DC） programming. Numerical simulations show that exponential metric function approximation yields better sparse recovery performance than other methods, and our proposed EMA-DC method is an efficient way to recover the sparse signals that are buried in noise.展开更多
基金Project (No. 10571154) supported by the National Natural ScienceFoundation of China
文摘In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4）^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.
基金supported in part by the National Natural Science Foundation of China (Nos. 61171120 and 61501504)the Key National Ministry Foundation of China (No. 9140A07020212JW0101)the Foundation of Tsinghua University (No. 20141081772)
文摘Sparse signal recovery problems are common in parameter estimation, image processing, pattern recognition, and so on. The problem of recovering a sparse signal representation from a signal dictionary might be classified as a linear constraint l_0-quasinorm minimization problem, which is thought to be a Non-deterministic Polynomial-time（NP）-hard problem. Although several approximation methods have been developed to solve this problem via convex relaxation, researchers find the nonconvex methods to be more efficient in solving sparse recovery problems than convex methods. In this paper a nonconvex Exponential Metric Approximation（EMA）method is proposed to solve the sparse signal recovery problem. Our proposed EMA method aims to minimize a nonconvex negative exponential metric function to attain the sparse approximation and, with proper transformation,solve the problem via Difference Convex（DC） programming. Numerical simulations show that exponential metric function approximation yields better sparse recovery performance than other methods, and our proposed EMA-DC method is an efficient way to recover the sparse signals that are buried in noise.
