### 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 language | English (US) |
---|---|

Pages (from-to) | 307-323 |

Number of pages | 17 |

Journal | Computers in Biology and Medicine |

Volume | 6 |

Issue number | 4 |

DOIs | |

State | Published - 1976 |

### Fingerprint

### 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

*Computers in Biology and Medicine*,

*6*(4), 307-323. https://doi.org/10.1016/0010-4825(76)90068-8

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

Research output: Contribution to journal › Article

*Computers in Biology and Medicine*, vol. 6, no. 4, pp. 307-323. https://doi.org/10.1016/0010-4825(76)90068-8

}

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

C2 - 1000957

AN - SCOPUS:0017005599

VL - 6

SP - 307

EP - 323

JO - Computers in Biology and Medicine

JF - Computers in Biology and Medicine

SN - 0010-4825

IS - 4

ER -