### Abstract

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

Original language | English (US) |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | L.E. Antonuk, M.J. Yaffe |

Pages | 339-349 |

Number of pages | 11 |

Volume | 4320 |

DOIs | |

State | Published - 2001 |

Event | Medical Imaging 2001: Physics of Medical Imaging - San Diego, CA, United States Duration: Feb 18 2001 → Feb 20 2001 |

### Other

Other | Medical Imaging 2001: Physics of Medical Imaging |
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Country | United States |

City | San Diego, CA |

Period | 2/18/01 → 2/20/01 |

### Fingerprint

### Keywords

- Detectability
- Digital radiography
- Image quality
- SNR

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(Vol. 4320, pp. 339-349) https://doi.org/10.1117/12.430932

**Analytical approximations to the Hotelling trace for digital x-ray detectors.** / Clarkson, Eric W; Pineda, A. R.; Barrett, Harrison H.

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

*Proceedings of SPIE - The International Society for Optical Engineering.*vol. 4320, pp. 339-349, Medical Imaging 2001: Physics of Medical Imaging, San Diego, CA, United States, 2/18/01. https://doi.org/10.1117/12.430932

}

TY - GEN

T1 - Analytical approximations to the Hotelling trace for digital x-ray detectors

AU - Clarkson, Eric W

AU - Pineda, A. R.

AU - Barrett, Harrison H

PY - 2001

Y1 - 2001

N2 - The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

AB - The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

KW - Detectability

KW - Digital radiography

KW - Image quality

KW - SNR

UR - http://www.scopus.com/inward/record.url?scp=0034865285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034865285&partnerID=8YFLogxK

U2 - 10.1117/12.430932

DO - 10.1117/12.430932

M3 - Conference contribution

AN - SCOPUS:0034865285

VL - 4320

SP - 339

EP - 349

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Antonuk, L.E.

A2 - Yaffe, M.J.

ER -