Compton camera imaging and the cone transform: A brief overview

Fatma Terzioglu, Peter Kuchment, Leonid Kunyansky

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

While most of Radon transform applications to imaging involve integrations over smooth sub-manifolds of the ambient space, lately important situations have appeared where the integration surfaces are conical. Three of such applications are single scatter optical tomography, Compton camera medical imaging, and homeland security. In spite of the similar surfaces of integration, the data and the inverse problems associated with these modalities differ significantly. In this article, we present a brief overview of the mathematics arising in Compton camera imaging. In particular, the emphasis is made on the overdetermined data and flexible geometry of the detectors. For the detailed results, as well as other approaches (e.g. smaller-dimensional data or restricted geometry of detectors) the reader is directed to the relevant publications. Only a brief description and some references are provided for the single scatter optical tomography.

Original languageEnglish (US)
Article number054002
JournalInverse Problems
Volume34
Issue number5
DOIs
StatePublished - Apr 3 2018

Fingerprint

Optical Tomography
Cones
Cone
Camera
Optical tomography
Cameras
Imaging
Transform
Scatter
Imaging techniques
Detector
Detectors
Homeland Security
Geometry
National security
Radon Transform
Medical Imaging
Radon
Medical imaging
Inverse problems

Keywords

  • Compton camera imaging
  • cone transform
  • radon transform

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Cite this

Compton camera imaging and the cone transform : A brief overview. / Terzioglu, Fatma; Kuchment, Peter; Kunyansky, Leonid.

In: Inverse Problems, Vol. 34, No. 5, 054002, 03.04.2018.

Research output: Contribution to journalArticle

Terzioglu, Fatma ; Kuchment, Peter ; Kunyansky, Leonid. / Compton camera imaging and the cone transform : A brief overview. In: Inverse Problems. 2018 ; Vol. 34, No. 5.
@article{0d62300e34f642ebabade4e185bb91d5,
title = "Compton camera imaging and the cone transform: A brief overview",
abstract = "While most of Radon transform applications to imaging involve integrations over smooth sub-manifolds of the ambient space, lately important situations have appeared where the integration surfaces are conical. Three of such applications are single scatter optical tomography, Compton camera medical imaging, and homeland security. In spite of the similar surfaces of integration, the data and the inverse problems associated with these modalities differ significantly. In this article, we present a brief overview of the mathematics arising in Compton camera imaging. In particular, the emphasis is made on the overdetermined data and flexible geometry of the detectors. For the detailed results, as well as other approaches (e.g. smaller-dimensional data or restricted geometry of detectors) the reader is directed to the relevant publications. Only a brief description and some references are provided for the single scatter optical tomography.",
keywords = "Compton camera imaging, cone transform, radon transform",
author = "Fatma Terzioglu and Peter Kuchment and Leonid Kunyansky",
year = "2018",
month = "4",
day = "3",
doi = "10.1088/1361-6420/aab0ab",
language = "English (US)",
volume = "34",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "IOP Publishing Ltd.",
number = "5",

}

TY - JOUR

T1 - Compton camera imaging and the cone transform

T2 - A brief overview

AU - Terzioglu, Fatma

AU - Kuchment, Peter

AU - Kunyansky, Leonid

PY - 2018/4/3

Y1 - 2018/4/3

N2 - While most of Radon transform applications to imaging involve integrations over smooth sub-manifolds of the ambient space, lately important situations have appeared where the integration surfaces are conical. Three of such applications are single scatter optical tomography, Compton camera medical imaging, and homeland security. In spite of the similar surfaces of integration, the data and the inverse problems associated with these modalities differ significantly. In this article, we present a brief overview of the mathematics arising in Compton camera imaging. In particular, the emphasis is made on the overdetermined data and flexible geometry of the detectors. For the detailed results, as well as other approaches (e.g. smaller-dimensional data or restricted geometry of detectors) the reader is directed to the relevant publications. Only a brief description and some references are provided for the single scatter optical tomography.

AB - While most of Radon transform applications to imaging involve integrations over smooth sub-manifolds of the ambient space, lately important situations have appeared where the integration surfaces are conical. Three of such applications are single scatter optical tomography, Compton camera medical imaging, and homeland security. In spite of the similar surfaces of integration, the data and the inverse problems associated with these modalities differ significantly. In this article, we present a brief overview of the mathematics arising in Compton camera imaging. In particular, the emphasis is made on the overdetermined data and flexible geometry of the detectors. For the detailed results, as well as other approaches (e.g. smaller-dimensional data or restricted geometry of detectors) the reader is directed to the relevant publications. Only a brief description and some references are provided for the single scatter optical tomography.

KW - Compton camera imaging

KW - cone transform

KW - radon transform

UR - http://www.scopus.com/inward/record.url?scp=85046542416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85046542416&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/aab0ab

DO - 10.1088/1361-6420/aab0ab

M3 - Article

AN - SCOPUS:85046542416

VL - 34

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 5

M1 - 054002

ER -