A NOTE ON MEYER-KONIG AND ZELLER OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION

In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.

A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS

Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.

Nemytskii Operator in the Space of Set-Valued Functions of Bounded <i>φ</i>-Variation

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.

Some Results on the Space of Bounded Second Variation Functions in the Sense of Shiba

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.

Uniformly Bounded Set-Valued Composition Operators in the Spaces of Functions of Bounded Variation in the Sense of Riesz

We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of Riesz, with nonempty bounded closed and convex values, are an affine function.

Generalized gap functions and error bounds for generalized variational inequalities

We consider some classes of generalized gap functions for two kinds of generalized variational inequality problems. We obtain error bounds for the underlying variational inequalities using the generalized gap functions under the condition that the involved mapping F is g-strongly monotone with respect to the solution, but not necessarily continuous differentiable, even not locally Lipschitz.

Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems

One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.

MEROMORPHIC FUNCTIONS WITH BOUNDED BOUNDARY ROTATION

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.

On Bounded Second Variation

In this paper, we discuss various aspects of the problem of space-invariance, under compositions, of certain subclasses of the space of all continuously differentiable functions on an interval [a,b] We present a result about integrability of products of the form gοf.f'f(k)under suitable mild conditions and, finally, we prove that a Nemytskij operator Sg maps BV''[a,b] a distinguished subspace of the space of all functions of second bounded variation, into itself if, and only if, g BV''loc(R) A similar result is obtained for the space of all functions of bounded (p,2)-variation (1≤p≤1),

On Bounded Variation Functions by General MKZD Operators

In this paper, we study the rate of convergence for functions of bounded variation for the recently introduced Bzier variant of the Meyer-Knig-Zeller-Durrmeyer operators.

Muntz Rational Approximation for Special Function Classes in Orlicz Spaces

Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.

MNTZ RATIONAL APPROXIMATION FOR SPECIAL FUNCTION CLASSES IN Ba[0,1] SPACES

In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.

Continuous Piecewise Linear Approximation of BV Function

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.

基于加权有界形变函数的可形变图像配准模型

可形变图像配准是图像处理领域中一个非常重要的课题,是计算机视觉中最基本的问题之一,也是医学图像分析的一个难题。文中研究了两幅单模态灰度图像之间的图像配准问题,充分考虑了参考图像的边缘信息,提出了一个新的基于加权有界形变函数的可形变图像配准模型。首次提出了加权的有界形变函数空间,给出了该空间的定义及相关结论,并从理论上证明了所提模型解的存在性。同时,利用梯度下降法设计了有效的算法进行数值求解,分别在合成图像和医学图像上进行数值实验。实验结果和定量评估结果表明,与对比模型相比,所提模型由于引入了控制函数且将加权有界形变函数作为正则项,得到了更精确的配准结果,特别是在图像边缘及一些细节处配准效果有明显提高。

基于Pochhammer k符号的Lupaş-Beta算子逼近性质

参数型基函数曲线曲面造型的应用与相应算子的结构性质和收敛性质被广泛关注。为此,本文首次利用Beta函数,构造了一种基于Pochhammer k符号的Lupas-Beta含幂参数型算子。同时,利用中心矩研究了该算子的Voronovskaya型渐进公式,根据Ditzian-Totik光滑模和Peetre’-K泛函讨论了其全局逼近,并借助函数的分解技巧和区间分割技术等研究了其关于导数为有界变差函数的点态估计。本研究将为该算子在曲线曲面造型中的应用提供关键的理论依据。

Mumford-Shah模型在图像分割中的研究

介绍了图像分割中的 Mumford- Shah(MS)模型 ,提出了一种新的 MS模型的数值求解方法。首先在数学上指出了 MS泛函弱解在 SBV函数空间中的存在性 ,然后讨论了计算弱解的数值逼近方法。为了得到 MS泛函的数值解 ,首先定义了自适应三角剖分空间上的离散型 MS泛函 ,然后在每次迭代前对有限元网格进行相应的自适应调整 ,接着采用拟牛顿最小化方法 ,并通过收敛意义上的离散有限元逼近 ,得到离散型 MS泛函在每次迭代中的最小值。实验结果表明 ,该方法适合含噪图像的分割 。

叙列空间上的k级囿变函数与k级绝对连续函数（I）

在［１］－［６］的基础上，考察了叙列空间上的ｋ级有界变差函数、ｋ级绝对连续函数的某些性质，连同它们与通常有界变差函数之间的关系．

基于变分的盲图像复原质量评价指标

盲图像复原过程中,图像质量评价至关重要.通过分析重构图像质量与其总变分值之间的关系,提出了用于图像复原的一种基于总变分(Total bounded variation,TBV)的图像质量评估方法,并构建关系模型,证明了原始清晰图像的总变分值在所有模糊图像中具有极大值,且在所有重构图像的变分值中具有极小值.通过分析,得出结论:当总变分取极值时,基于所提度量方法,可以获得更好的盲图像重构效果.最后,比较了原始清晰图像、模糊图像和重构图像之间的变分值,计算机仿真验证了该方法的有效性和准确性.

基于变分法的图像分割的数值算法(英文)

解释一种图像分割问题的数学模型 ,并讨论图像分割问题与Mumford Shah泛函的关系 ,对此问题首先就一维的情形提出一种可行的解法并推广到二维。若干试验结果验证了算法的有效性。

图像的多尺度几何分析概述

以函数的稀疏表示为主线,详细介绍了各种多尺度几何分析产生的背景、发展历程和逼近性能,并分析了它们各自存在的优缺点,最后指出了其发展方向。