Two-Stage Local Polynomial Regression Method for Image Heteroscedastic Noise Removal

2013 ◽  
Vol 860-863 ◽  
pp. 2936-2939
Author(s):  
Li Yun Su ◽  
Chun Hua Wang
Keyword(s):  
Regression Model ◽  
Polynomial Regression ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
Noise Removal ◽  
Local Polynomial Regression ◽  
Local Polynomial ◽  
Noise Function ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation

In this paper, we introduce the extension of local polynomial fitting to the linear heteroscedastic regression model and its applications in digital image heteroscedastic noise removal. For better image noise removal with heteroscedastic energy, firstly, the local polynomial regression is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. Due to non-parametric technique of local polynomial estimation, we do not need to know the heteroscedastic noise function. Therefore, we improve the estimation precision, when the heteroscedastic noise function is unknown. Numerical simulations results show that the proposed method can improve the image quality of heteroscedastic noise energy.

scholarly journals Two-Stage Method Based on Local Polynomial Fitting for a Linear Heteroscedastic Regression Model and Its Application in Economics

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Liyun Su ◽  
Yanyong Zhao ◽  
Tianshun Yan
Keyword(s):  
Regression Model ◽  
Least Squares Method ◽  
Generalized Least Squares ◽  
Finite Sample ◽  
Local Polynomial Fitting ◽  
Polynomial Fitting ◽  
Two Stage ◽  
Local Polynomial ◽  
Heteroscedastic Regression ◽  
Local Polynomial Estimation

We introduce the extension of local polynomial fitting to the linear heteroscedastic regression model. Firstly, the local polynomial fitting is applied to estimate heteroscedastic function, then the coefficients of regression model are obtained by using generalized least squares method. One noteworthy feature of our approach is that we avoid the testing for heteroscedasticity by improving the traditional two-stage method. Due to nonparametric technique of local polynomial estimation, we do not need to know the heteroscedastic function. Therefore, we can improve the estimation precision, when the heteroscedastic function is unknown. Furthermore, we focus on comparison of parameters and reach an optimal fitting. Besides, we verify the asymptotic normality of parameters based on numerical simulations. Finally, this approach is applied to a case of economics, and it indicates that our method is surely effective in finite-sample situations.

scholarly journals To the Issue of Determining Agricultural Tractor Slipping

2021 ◽  
pp. 14-18
Author(s):  
A.B. Ivanov ◽  
◽  
V.E. Tarkivsky ◽  
V.Yu. Revenko ◽  
◽  
...  
Keyword(s):  
Regression Analysis ◽  
Regression Model ◽  
Polynomial Regression ◽  
Local Polynomial Regression ◽  
Local Polynomial ◽  
Agricultural Tractors ◽  
Engine Crankshaft ◽  
Agricultural Tractor

The well-known methods for determining the slipping of the propulsion devices of agricultural tractors are described. A regression analysis of the traction characteristics of a wheeled tractor is performed. The equivalence of the method for determining the current slippage through the actual tractor speed and engine crankshaft speed is assessed. A regression model is proposed to determine the amount of slippage based on the method of local polynomial regression (locally estimated scatterplot smoothing or LOESS)

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