### Abstract

Image statistics are usually modeled as Poisson in γ-ray imaging and as Gaussian in x-ray imaging. In nuclear medicine, event-driven detectors analyze the pulses from every absorbed gamma photon individually; the resulting images rigorously obey Poisson statistics but are approximately Gaussian when the mean number of counts per pixel is large. With integrating detectors, as in digital radiography, each x-ray photon makes a contribution to the image proportional to its pulse height. One pixel senses many photons in long exposures, so the image statistics approach Gaussian by the central limit theorem (CLT). If the exposure time is short enough, however, each pixel will usually respond to no more than one photon, and we can separate individual photons for position estimation. Integrating detectors are therefore event-driven when we use many short-exposure frames rather than one long exposure. In intermediate exposures, the number of photons in one pixel is too small to invoke CLT and apply Gaussian statistics, yet too large to identify individual photons and apply Poisson statistics. In this paper, we analyze the image quality in this intermediate case. Image quality is defined for detection tasks performed by the ideal observer. Because the frames in a data set are independent of each other, the probability density function (PDF) of the whole data set is a product of the frame PDFs. The log-likelihood ratio A of the ideal observer is thus a sum across the frames and has Gaussian statistics even with non-Gaussian images. We compare the ideal observer's performance with the Hotelling observer's performance under this approximation. A data-thresholding technique to improve Hotelling observer's performance is also discussed.

Original language | English (US) |
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Title of host publication | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |

Editors | M.J. Flynn |

Pages | 366-376 |

Number of pages | 11 |

Volume | 5745 |

Edition | I |

DOIs | |

State | Published - 2005 |

Event | Medical Imaging 2005 - Physics of Medical Imaging - San Diego, CA, United States Duration: Feb 13 2005 → Feb 15 2005 |

### Other

Other | Medical Imaging 2005 - Physics of Medical Imaging |
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Country | United States |

City | San Diego, CA |

Period | 2/13/05 → 2/15/05 |

### Fingerprint

### Keywords

- Event-driven detector
- Frame time
- Ideal observer
- Image quality
- Integrating detector
- Log-likelihood ratio
- Non-Gaussian noise
- Threshold

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(I ed., Vol. 5745, pp. 366-376). [44] https://doi.org/10.1117/12.589396

**Non-Gaussian noise in x-ray and γ-ray detectors.** / Chen, Liying; Barrett, Harrison H.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE.*I edn, vol. 5745, 44, pp. 366-376, Medical Imaging 2005 - Physics of Medical Imaging, San Diego, CA, United States, 2/13/05. https://doi.org/10.1117/12.589396

}

TY - GEN

T1 - Non-Gaussian noise in x-ray and γ-ray detectors

AU - Chen, Liying

AU - Barrett, Harrison H

PY - 2005

Y1 - 2005

N2 - Image statistics are usually modeled as Poisson in γ-ray imaging and as Gaussian in x-ray imaging. In nuclear medicine, event-driven detectors analyze the pulses from every absorbed gamma photon individually; the resulting images rigorously obey Poisson statistics but are approximately Gaussian when the mean number of counts per pixel is large. With integrating detectors, as in digital radiography, each x-ray photon makes a contribution to the image proportional to its pulse height. One pixel senses many photons in long exposures, so the image statistics approach Gaussian by the central limit theorem (CLT). If the exposure time is short enough, however, each pixel will usually respond to no more than one photon, and we can separate individual photons for position estimation. Integrating detectors are therefore event-driven when we use many short-exposure frames rather than one long exposure. In intermediate exposures, the number of photons in one pixel is too small to invoke CLT and apply Gaussian statistics, yet too large to identify individual photons and apply Poisson statistics. In this paper, we analyze the image quality in this intermediate case. Image quality is defined for detection tasks performed by the ideal observer. Because the frames in a data set are independent of each other, the probability density function (PDF) of the whole data set is a product of the frame PDFs. The log-likelihood ratio A of the ideal observer is thus a sum across the frames and has Gaussian statistics even with non-Gaussian images. We compare the ideal observer's performance with the Hotelling observer's performance under this approximation. A data-thresholding technique to improve Hotelling observer's performance is also discussed.

AB - Image statistics are usually modeled as Poisson in γ-ray imaging and as Gaussian in x-ray imaging. In nuclear medicine, event-driven detectors analyze the pulses from every absorbed gamma photon individually; the resulting images rigorously obey Poisson statistics but are approximately Gaussian when the mean number of counts per pixel is large. With integrating detectors, as in digital radiography, each x-ray photon makes a contribution to the image proportional to its pulse height. One pixel senses many photons in long exposures, so the image statistics approach Gaussian by the central limit theorem (CLT). If the exposure time is short enough, however, each pixel will usually respond to no more than one photon, and we can separate individual photons for position estimation. Integrating detectors are therefore event-driven when we use many short-exposure frames rather than one long exposure. In intermediate exposures, the number of photons in one pixel is too small to invoke CLT and apply Gaussian statistics, yet too large to identify individual photons and apply Poisson statistics. In this paper, we analyze the image quality in this intermediate case. Image quality is defined for detection tasks performed by the ideal observer. Because the frames in a data set are independent of each other, the probability density function (PDF) of the whole data set is a product of the frame PDFs. The log-likelihood ratio A of the ideal observer is thus a sum across the frames and has Gaussian statistics even with non-Gaussian images. We compare the ideal observer's performance with the Hotelling observer's performance under this approximation. A data-thresholding technique to improve Hotelling observer's performance is also discussed.

KW - Event-driven detector

KW - Frame time

KW - Ideal observer

KW - Image quality

KW - Integrating detector

KW - Log-likelihood ratio

KW - Non-Gaussian noise

KW - Threshold

UR - http://www.scopus.com/inward/record.url?scp=23844459367&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23844459367&partnerID=8YFLogxK

U2 - 10.1117/12.589396

DO - 10.1117/12.589396

M3 - Conference contribution

AN - SCOPUS:23844459367

VL - 5745

SP - 366

EP - 376

BT - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

A2 - Flynn, M.J.

ER -