Statistical limitations in transaxial tomography

Harrison H Barrett, S. K. Gordon, R. S. Hershel

Research output: Contribution to journalArticle

98 Citations (Scopus)

Abstract

A general analysis is presented of the limitations on transaxial tomographic imaging due to the quantum statistics of the radiation source. An idealized model is used in which reconstruction errors due to divergence of the X-ray beam, the finite number of projections, and the finite detector size are neglected. The results, therefore, represent an upper bound to the performance attainable with this method. An operator formalism is introduced to describe the various linear reconstruction algorithms, all of which are shown to be statistically equivalent. Expressions are derived for the mean signal, rms noise, resolution, and required radiation dose for a given signal-to-noise ratio. The results are valid for any object and any linear reconstruction algorithm.

Original languageEnglish (US)
Pages (from-to)307-323
Number of pages17
JournalComputers in Biology and Medicine
Volume6
Issue number4
DOIs
StatePublished - 1976

Fingerprint

Tomography
Radiation
Signal-To-Noise Ratio
Dosimetry
Noise
Signal to noise ratio
X-Rays
Statistics
Detectors
Imaging techniques
X rays

Keywords

  • Divergent X-ray beam
  • Dose scaling
  • Linear reconstruction algorithms
  • Resolution limitations
  • Signal-to-noise ratio
  • Statistical limitations
  • Transaxial tomography

ASJC Scopus subject areas

  • Computer Science Applications

Cite this

Statistical limitations in transaxial tomography. / Barrett, Harrison H; Gordon, S. K.; Hershel, R. S.

In: Computers in Biology and Medicine, Vol. 6, No. 4, 1976, p. 307-323.

Research output: Contribution to journalArticle

Barrett, Harrison H ; Gordon, S. K. ; Hershel, R. S. / Statistical limitations in transaxial tomography. In: Computers in Biology and Medicine. 1976 ; Vol. 6, No. 4. pp. 307-323.
@article{755e09cc46694aba898d98cdc497ab3e,
title = "Statistical limitations in transaxial tomography",
abstract = "A general analysis is presented of the limitations on transaxial tomographic imaging due to the quantum statistics of the radiation source. An idealized model is used in which reconstruction errors due to divergence of the X-ray beam, the finite number of projections, and the finite detector size are neglected. The results, therefore, represent an upper bound to the performance attainable with this method. An operator formalism is introduced to describe the various linear reconstruction algorithms, all of which are shown to be statistically equivalent. Expressions are derived for the mean signal, rms noise, resolution, and required radiation dose for a given signal-to-noise ratio. The results are valid for any object and any linear reconstruction algorithm.",
keywords = "Divergent X-ray beam, Dose scaling, Linear reconstruction algorithms, Resolution limitations, Signal-to-noise ratio, Statistical limitations, Transaxial tomography",
author = "Barrett, {Harrison H} and Gordon, {S. K.} and Hershel, {R. S.}",
year = "1976",
doi = "10.1016/0010-4825(76)90068-8",
language = "English (US)",
volume = "6",
pages = "307--323",
journal = "Computers in Biology and Medicine",
issn = "0010-4825",
publisher = "Elsevier Limited",
number = "4",

}

TY - JOUR

T1 - Statistical limitations in transaxial tomography

AU - Barrett, Harrison H

AU - Gordon, S. K.

AU - Hershel, R. S.

PY - 1976

Y1 - 1976

N2 - A general analysis is presented of the limitations on transaxial tomographic imaging due to the quantum statistics of the radiation source. An idealized model is used in which reconstruction errors due to divergence of the X-ray beam, the finite number of projections, and the finite detector size are neglected. The results, therefore, represent an upper bound to the performance attainable with this method. An operator formalism is introduced to describe the various linear reconstruction algorithms, all of which are shown to be statistically equivalent. Expressions are derived for the mean signal, rms noise, resolution, and required radiation dose for a given signal-to-noise ratio. The results are valid for any object and any linear reconstruction algorithm.

AB - A general analysis is presented of the limitations on transaxial tomographic imaging due to the quantum statistics of the radiation source. An idealized model is used in which reconstruction errors due to divergence of the X-ray beam, the finite number of projections, and the finite detector size are neglected. The results, therefore, represent an upper bound to the performance attainable with this method. An operator formalism is introduced to describe the various linear reconstruction algorithms, all of which are shown to be statistically equivalent. Expressions are derived for the mean signal, rms noise, resolution, and required radiation dose for a given signal-to-noise ratio. The results are valid for any object and any linear reconstruction algorithm.

KW - Divergent X-ray beam

KW - Dose scaling

KW - Linear reconstruction algorithms

KW - Resolution limitations

KW - Signal-to-noise ratio

KW - Statistical limitations

KW - Transaxial tomography

UR - http://www.scopus.com/inward/record.url?scp=0017005599&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0017005599&partnerID=8YFLogxK

U2 - 10.1016/0010-4825(76)90068-8

DO - 10.1016/0010-4825(76)90068-8

M3 - Article

VL - 6

SP - 307

EP - 323

JO - Computers in Biology and Medicine

JF - Computers in Biology and Medicine

SN - 0010-4825

IS - 4

ER -