### Abstract

The asymptotic form for the likelihood ratio is derived for list-mode data generated by an imaging system viewing a possible signal in a randomly generated background. This calculation provides an approximation to the likelihood ratio that is valid in the limit of large number of list entries, i.e., a large number of photons. These results are then used to derive surrogate figures of merit, quantities that are correlated with ideal-observer performance on detection tasks, as measured by the area under the receiver operating characteristic curve, but are easier to compute. A key component of these derivations is the determination of asymptotic forms for the Fisher information for the signal amplitude in the limit of a large number of counts or a long exposure time. This quantity is useful in its own right as a figure of merit (FOM) for the task of estimating the signal amplitude. The use of the Fisher information in detection tasks is based on the fact that it provides an approximation for ideal-observer detectability when the signal is weak. For both the fixed-count and fixed-time cases, four surrogate figures of merit are derived. Two are based on maximum likelihood reconstructions; one uses the characteristic functional of the random backgrounds. The fourth surrogate FOM is identical in the two cases and involves an integral over attribute space for each of a randomly generated sequence of backgrounds.

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

Pages (from-to) | 2204-2216 |

Number of pages | 13 |

Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |

Volume | 29 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2012 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Electronic, Optical and Magnetic Materials
- Computer Vision and Pattern Recognition
- Medicine(all)

### Cite this

**Asymptotic ideal observers and surrogate figures of merit for signal detection with list-mode data.** / Clarkson, Eric W.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Asymptotic ideal observers and surrogate figures of merit for signal detection with list-mode data

AU - Clarkson, Eric W

PY - 2012/10/1

Y1 - 2012/10/1

N2 - The asymptotic form for the likelihood ratio is derived for list-mode data generated by an imaging system viewing a possible signal in a randomly generated background. This calculation provides an approximation to the likelihood ratio that is valid in the limit of large number of list entries, i.e., a large number of photons. These results are then used to derive surrogate figures of merit, quantities that are correlated with ideal-observer performance on detection tasks, as measured by the area under the receiver operating characteristic curve, but are easier to compute. A key component of these derivations is the determination of asymptotic forms for the Fisher information for the signal amplitude in the limit of a large number of counts or a long exposure time. This quantity is useful in its own right as a figure of merit (FOM) for the task of estimating the signal amplitude. The use of the Fisher information in detection tasks is based on the fact that it provides an approximation for ideal-observer detectability when the signal is weak. For both the fixed-count and fixed-time cases, four surrogate figures of merit are derived. Two are based on maximum likelihood reconstructions; one uses the characteristic functional of the random backgrounds. The fourth surrogate FOM is identical in the two cases and involves an integral over attribute space for each of a randomly generated sequence of backgrounds.

AB - The asymptotic form for the likelihood ratio is derived for list-mode data generated by an imaging system viewing a possible signal in a randomly generated background. This calculation provides an approximation to the likelihood ratio that is valid in the limit of large number of list entries, i.e., a large number of photons. These results are then used to derive surrogate figures of merit, quantities that are correlated with ideal-observer performance on detection tasks, as measured by the area under the receiver operating characteristic curve, but are easier to compute. A key component of these derivations is the determination of asymptotic forms for the Fisher information for the signal amplitude in the limit of a large number of counts or a long exposure time. This quantity is useful in its own right as a figure of merit (FOM) for the task of estimating the signal amplitude. The use of the Fisher information in detection tasks is based on the fact that it provides an approximation for ideal-observer detectability when the signal is weak. For both the fixed-count and fixed-time cases, four surrogate figures of merit are derived. Two are based on maximum likelihood reconstructions; one uses the characteristic functional of the random backgrounds. The fourth surrogate FOM is identical in the two cases and involves an integral over attribute space for each of a randomly generated sequence of backgrounds.

UR - http://www.scopus.com/inward/record.url?scp=84867552626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867552626&partnerID=8YFLogxK

U2 - 10.1364/JOSAA.29.002204

DO - 10.1364/JOSAA.29.002204

M3 - Article

C2 - 23201670

AN - SCOPUS:84867552626

VL - 29

SP - 2204

EP - 2216

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 10

ER -