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

Katharina Proksch

doi:10.1063/1.4825596

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

Katharina Proksch

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

Abstract

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).

Original language	English
Title of host publication	11th International Conference of Numerical Analysis and Applied Mathematics 2013
Subtitle of host publication	ICNAAM 2013
Editors	Theodore Simos, George Psihoyios, Ch. Tsitouras
Publisher	American Institute of Physics
Pages	728-731
ISBN (Print)	978-0-7354-1184-5
DOIs	https://doi.org/10.1063/1.4825596
Publication status	Published - 2013
Event	11th International Conference of Numerical Analysis and Applied Mathematics 2013 - Rodos Palace Hotel, Rhodes, Greece Duration: 21 Sept 2013 → 27 Sept 2013 Conference number: 11 http://history.icnaam.org/icnaam_2013/index.htm

Publication series

Name	AIP Conference Proceedings
Publisher	AIP
Volume	1558
ISSN (Print)	0094-243X

Conference

Conference	11th International Conference of Numerical Analysis and Applied Mathematics 2013
Abbreviated title	ICNAAM 2013
Country/Territory	Greece
City	Rhodes
Period	21/09/13 → 27/09/13
Internet address	http://history.icnaam.org/icnaam_2013/index.htm

Keywords

Inverse problems
Multivariate regression
Nonparametric regression
Radon transform

Access to Document

10.1063/1.4825596

Cite this

Proksch, K. (2013). Asymptotic Normality of Kernel Estimators for Images Observed under the Radon Transform in Fan Beam Design. In T. Simos, G. Psihoyios, & C. Tsitouras (Eds.), 11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013 (pp. 728-731). (AIP Conference Proceedings; Vol. 1558). American Institute of Physics. https://doi.org/10.1063/1.4825596

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

abstract = "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).",

keywords = "Inverse problems, Multivariate regression, Nonparametric regression, Radon transform",

author = "Katharina Proksch",

year = "2013",

doi = "10.1063/1.4825596",

language = "English",

isbn = "978-0-7354-1184-5",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

pages = "728--731",

editor = "Theodore Simos and George Psihoyios and Ch. Tsitouras",

booktitle = "11th International Conference of Numerical Analysis and Applied Mathematics 2013",

address = "United States",

note = "11th International Conference of Numerical Analysis and Applied Mathematics 2013, ICNAAM 2013 ; Conference date: 21-09-2013 Through 27-09-2013",

url = "http://history.icnaam.org/icnaam\_2013/index.htm",

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Proksch, K 2013, Asymptotic Normality of Kernel Estimators for Images Observed under the Radon Transform in Fan Beam Design. in T Simos, G Psihoyios & C Tsitouras (eds), 11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013. AIP Conference Proceedings, vol. 1558, American Institute of Physics, pp. 728-731, 11th International Conference of Numerical Analysis and Applied Mathematics 2013, Rhodes, Greece, 21/09/13. https://doi.org/10.1063/1.4825596

Asymptotic Normality of Kernel Estimators for Images Observed under the Radon Transform in Fan Beam Design. / Proksch, Katharina.
11th International Conference of Numerical Analysis and Applied Mathematics 2013: ICNAAM 2013. ed. / Theodore Simos; George Psihoyios; Ch. Tsitouras. American Institute of Physics, 2013. p. 728-731 (AIP Conference Proceedings; Vol. 1558).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Proksch, Katharina

N1 - Conference code: 11

PY - 2013

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N2 - 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).

AB - 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).

KW - Inverse problems

KW - Multivariate regression

KW - Nonparametric regression

KW - Radon transform

U2 - 10.1063/1.4825596

DO - 10.1063/1.4825596

M3 - Conference contribution

SN - 978-0-7354-1184-5

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EP - 731

BT - 11th International Conference of Numerical Analysis and Applied Mathematics 2013

A2 - Simos, Theodore

A2 - Psihoyios, George

A2 - Tsitouras, Ch.

PB - American Institute of Physics

T2 - 11th International Conference of Numerical Analysis and Applied Mathematics 2013

Y2 - 21 September 2013 through 27 September 2013

ER -

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

Abstract

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Conference

Keywords

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