### 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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Pages (from-to) | 339-349 |

Number of pages | 11 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 4320 |

DOIs | |

State | Published - Jan 1 2001 |

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

### Keywords

- Detectability
- Digital radiography
- Image quality
- SNR

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering