Asymptotic Normality of Kernel Estimators for Images Observed under the Radon Transform in Fan Beam Design

被引：0

作者：

Proksch, Katharina ^{[1
]}

机构：

[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

来源：

11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013, PTS 1 AND 2 (ICNAAM 2013) | 2013年 / 1558卷

关键词：

Inverse problems; Multivariate regression; Nonparametric regression; Radon transform;

D O I：

10.1063/1.4825596

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a nonparametric, two-dimensional regression model that describes observations of Radon transformed images, i.e., an inverse regression model. Reconstructions from deterministic fan beam design by a certain kind of kernel-type estimators are considered and their asymptotic properties are investigated. The problem discussed is related to medical imaging procedures such as computerized tomography (CT).

引用

页码：728 / 731

页数：4

共 50 条

[1] Asymptotic normality of kernel density estimators under dependence
Lu, ZD
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2001, 53 (03) : 447 - 468
[2] Asymptotic Normality of Kernel Density Estimators under Dependence
Zudi Lu
Annals of the Institute of Statistical Mathematics, 2001, 53 : 447 - 468
[3] ASYMPTOTIC NORMALITY FOR DECONVOLUTION KERNEL DENSITY ESTIMATORS
FAN, JQ
SANKHYA-THE INDIAN JOURNAL OF STATISTICS SERIES A, 1991, 53 : 97 - 110
[4] On the asymptotic normality of the kernel estimators of the density function and its derivatives under censoring
Louani, D
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1998, 27 (12) : 2909 - 2924
[5] Asymptotic normality of kernel estimators of the conditional mode under strong mixing hypothesis
Louani, D
Ould-Saïd, E
JOURNAL OF NONPARAMETRIC STATISTICS, 1999, 11 (04) : 413 - 442
[6] On the rates of asymptotic normality for recursive kernel density estimators under φ-mixing assumptions
Xi, Mengmei
Wang, Xuejun
JOURNAL OF NONPARAMETRIC STATISTICS, 2019, 31 (02) : 340 - 363
[7] Confidence regions for images observed under the Radon transform
Bissantz, Nicolai
Holzmann, Hajo
Proksch, Katharina
JOURNAL OF MULTIVARIATE ANALYSIS, 2014, 128 : 86 - 107
[8] On the asymptotic normality of kernel regression estimators of the mode in the nonparametric random design model
Ziegler, K
JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2003, 115 (01) : 123 - 144
[9] Asymptotic normality of kernel-type deconvolution estimators
van Es, B
Uh, HW
SCANDINAVIAN JOURNAL OF STATISTICS, 2005, 32 (03) : 467 - 483
[10] Asymptotic normality of kernel estimators based upon incomplete data
Boukeloua, M.
Messaci, F.
JOURNAL OF NONPARAMETRIC STATISTICS, 2016, 28 (03) : 469 - 486

← 1 2 3 4 5 →