In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bou...In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.展开更多
Image fusion is important in computer vision where the main goal is to integrate several sources images of the same scene into a more informative image. In this paper, we propose a variational image fusion method base...Image fusion is important in computer vision where the main goal is to integrate several sources images of the same scene into a more informative image. In this paper, we propose a variational image fusion method based on the first and second-order gradient information. Firstly, we select the target first-order and second-order gradient information from the source images by a new and simple salience criterion. Then we build our model by requiring that the first-order and second-order gradient information of the fused image match with the target gradient information, and meanwhile the fused image is close to the source images. Theoretically, we can prove that our variational model has a unique minimizer. In the numerical implementation, we take use of the split Bregman method to get an efficient algorithm. Moreover, four-direction difference scheme is proposed to discrete gradient operator, which can dramatically enhance the fusion quality. A number of experiments and comparisons with some popular existing methods demonstrate that the proposed model is promising in various image fusion applications.展开更多
In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space...In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space be closed under composition of functions. Another significant result is the proof that this space of bounded second variation in the sense of Shiba is a Banach algebra, which is not immediate as it happens in other spaces of generalized bounded variation.展开更多
New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are give...New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regularization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.展开更多
In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.
The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators Mn,k for functions of bounded variation, by using some techniques of p...The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators Mn,k for functions of bounded variation, by using some techniques of probability theory.展开更多
We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integr...We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.展开更多
We discuss the relations among the best approximation En(f) and the Fourier coeffcients of a function, f(n) ∈ C,n = 0,±1,±2,..., under the conditions that {f (n)}∞n=0 ∈ MVBVS* and {f (n) + f(n)}∞n=0 ∈ M...We discuss the relations among the best approximation En(f) and the Fourier coeffcients of a function, f(n) ∈ C,n = 0,±1,±2,..., under the conditions that {f (n)}∞n=0 ∈ MVBVS* and {f (n) + f(n)}∞n=0 ∈ MVBVS*, where MVBVS* is the class of the so-called Strong Mean Value Bounded Variation Sequences.展开更多
Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by bal...Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The results of experiments show that this new method is superior to the old one.展开更多
文摘In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.
基金Acknowledgments. This work is supported by the 973 Program （2011CB707104）, the Science and Technology Commission of Shanghai Municipality （STCSM） 13dz2260400, the National Science Foundation of China （Nos. 11001082, 11271049）, and RGC 211710, 211911, 12302714 and RFGs of HKBU.
文摘Image fusion is important in computer vision where the main goal is to integrate several sources images of the same scene into a more informative image. In this paper, we propose a variational image fusion method based on the first and second-order gradient information. Firstly, we select the target first-order and second-order gradient information from the source images by a new and simple salience criterion. Then we build our model by requiring that the first-order and second-order gradient information of the fused image match with the target gradient information, and meanwhile the fused image is close to the source images. Theoretically, we can prove that our variational model has a unique minimizer. In the numerical implementation, we take use of the split Bregman method to get an efficient algorithm. Moreover, four-direction difference scheme is proposed to discrete gradient operator, which can dramatically enhance the fusion quality. A number of experiments and comparisons with some popular existing methods demonstrate that the proposed model is promising in various image fusion applications.
文摘In this paper, we study the structure of the space of functions of bounded second variation in the sense of Shiba;an integral representation theorem is also proved and necessary conditions are given for that the space be closed under composition of functions. Another significant result is the proof that this space of bounded second variation in the sense of Shiba is a Banach algebra, which is not immediate as it happens in other spaces of generalized bounded variation.
文摘New models for image decomposition are proposed which separate an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed models are given in a variational formulation with adaptive regularization norms for both the cartoon and texture parts. The adaptive behavior preserves key features such as object boundaries and textures while avoiding staircasing in what should be smooth regions. This decomposition is computed by minimizing a convex functional which depends on the two variables u and v, alternatively in each variable. Experimental results and comparisons to validate the proposed models are presented.
基金partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge
文摘In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given.
文摘The present paper deals with the new type of Gamma operators, here we estimate the rate of pointwise convergence of these new Gamma type operators Mn,k for functions of bounded variation, by using some techniques of probability theory.
文摘We know that the Box dimension of f（x） ∈ C^1[0,1] is 1. In this paper, we prove that the Box dimension of continuous functions with bounded variation is still 1. Furthermore, Box dimension of Weyl fractional integral of above function is also 1.
基金NSERC RCD grant and AARMS of Canada (Yu D S)by NSERC of Canada(Zhou P)+2 种基金by the National Natural Science Foundation of China (Grant No. 10471130)the Open Fund(Grant No. PLN0613) of State Key Laboratory of OilGas Reservoir Geology and Exploitation (Southwest Petroleum University) (Zhou S P)
文摘We discuss the relations among the best approximation En(f) and the Fourier coeffcients of a function, f(n) ∈ C,n = 0,±1,±2,..., under the conditions that {f (n)}∞n=0 ∈ MVBVS* and {f (n) + f(n)}∞n=0 ∈ MVBVS*, where MVBVS* is the class of the so-called Strong Mean Value Bounded Variation Sequences.
文摘Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be self- adaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The results of experiments show that this new method is superior to the old one.
