局部平均概率型算子线性组合的点态逼近  

Pointwise Approximation for Linear Combination of Probabilistic Operators on Local Averages

作　　者：宋占杰[1] 倪平[1] 杨寿渊[2] 

机构地区：[1]天津大学理学院,天津300072 [2]南开大学数学系,天津300071

出　　处：《天津大学学报》2005年第11期1031-1034,共4页Journal of Tianjin University(Science and Technology)

基　　金：数学天元基金资助项目(10426020)南开大学-天津大学刘徽应用数学中心资助项目.

摘　　要：现代数字信号(包括图像)的处理是基于原始信号f(x)的一组局部平均离散采样值．这种局部平均采样 可以有效地抑制高频噪声的影响．由二项过程、泊松过程和负二项过程导出的局部平均概率型算子是在采样点处 的一种局部积分平均．为此,研究了这种算子线性组合的点态逼近,得到了误差的阶和新的Ditzian光滑模之间的 等价关系．Modern digital data processing of functions （include signals and images） can be carried out with a discrete version of the original signalf（x） obtained by sampling a discrete set of local averages. The influence of high frequency noise can be suppressed by the local average sampling. Probabilistic operators on local averages, which are constructed by binomial processes, Poisson processes and negative binomial processes, are a kind of local averages at the time point by integration. Study on the pointwise approximation for linear combinations of these operators shows the equivalence between the order of error and the new modulus of Ditzian.

关 键 词：概率型算子 局部平均值 点态逼近 光滑模 

分 类 号：O211[理学—概率论与数理统计] O174[理学—数学]