### Abstract

An expression is derived showing that the two-dimensional noise power spectrum of computed X-ray tomography is proportional to mod G(k) mod ^{2}/k where k is the radial spatial frequency and G(k) is the one-dimensional corrective filter used in the filtered back-projection reconstruction technique. It is shown that predicted noise power spectra compare well with those estimated from CT reconstructions of simulated noise for both the ramp filter and the Hanning-weighted ramp filter. A consequence of the non-uniform shape of the noise power spectrum is that statistical noise in CT reconstructions is correlated from point to point. Because of this correlation when the reconstructed CT values are averaged over some region, the uncertainty of the average depends on the shape of the region as well as its area. This dependence is confirmed by computer simulations.

Original language | English (US) |
---|---|

Article number | 008 |

Pages (from-to) | 446-454 |

Number of pages | 9 |

Journal | Physics in Medicine and Biology |

Volume | 23 |

Issue number | 3 |

DOIs | |

State | Published - 1978 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Biomedical Engineering
- Radiology Nuclear Medicine and imaging
- Physics and Astronomy (miscellaneous)
- Radiological and Ultrasound Technology

### Cite this

*Physics in Medicine and Biology*,

*23*(3), 446-454. [008]. https://doi.org/10.1088/0031-9155/23/3/008

**The noise power spectrum in computed X-ray tomography.** / Riederer, Stephen J; Pelc, N. J.; Chesler, D. A.

Research output: Contribution to journal › Article

*Physics in Medicine and Biology*, vol. 23, no. 3, 008, pp. 446-454. https://doi.org/10.1088/0031-9155/23/3/008

}

TY - JOUR

T1 - The noise power spectrum in computed X-ray tomography

AU - Riederer, Stephen J

AU - Pelc, N. J.

AU - Chesler, D. A.

PY - 1978

Y1 - 1978

N2 - An expression is derived showing that the two-dimensional noise power spectrum of computed X-ray tomography is proportional to mod G(k) mod 2/k where k is the radial spatial frequency and G(k) is the one-dimensional corrective filter used in the filtered back-projection reconstruction technique. It is shown that predicted noise power spectra compare well with those estimated from CT reconstructions of simulated noise for both the ramp filter and the Hanning-weighted ramp filter. A consequence of the non-uniform shape of the noise power spectrum is that statistical noise in CT reconstructions is correlated from point to point. Because of this correlation when the reconstructed CT values are averaged over some region, the uncertainty of the average depends on the shape of the region as well as its area. This dependence is confirmed by computer simulations.

AB - An expression is derived showing that the two-dimensional noise power spectrum of computed X-ray tomography is proportional to mod G(k) mod 2/k where k is the radial spatial frequency and G(k) is the one-dimensional corrective filter used in the filtered back-projection reconstruction technique. It is shown that predicted noise power spectra compare well with those estimated from CT reconstructions of simulated noise for both the ramp filter and the Hanning-weighted ramp filter. A consequence of the non-uniform shape of the noise power spectrum is that statistical noise in CT reconstructions is correlated from point to point. Because of this correlation when the reconstructed CT values are averaged over some region, the uncertainty of the average depends on the shape of the region as well as its area. This dependence is confirmed by computer simulations.

UR - http://www.scopus.com/inward/record.url?scp=0017800671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0017800671&partnerID=8YFLogxK

U2 - 10.1088/0031-9155/23/3/008

DO - 10.1088/0031-9155/23/3/008

M3 - Article

C2 - 674361

AN - SCOPUS:0017800671

VL - 23

SP - 446

EP - 454

JO - Physics in Medicine and Biology

JF - Physics in Medicine and Biology

SN - 0031-9155

IS - 3

M1 - 008

ER -