### Abstract

In medical imaging, signal detection is one of the most important tasks. A common way to evaluate the performance of an imaging system for a signal-detection task is to calculate the detectability of the ideal observer. Since the detectability of an ideal observer is not always easy to calculate, it is useful to have approximations for it. These approximations can also be used to check the bias of numerical computations of the ideal-observer detectability. For signal detection tasks, we usually have two probability densities for the data vector, the signal-absent density and the signal-present density. In this work, we use a single probability density with a variable scalar or vector parameter to represent the corresponding densities under the two hypotheses. The ideal-observer detectability is derived from the area under the receiver operating characteristic curve of the ideal observer for the given detection task. We have found that we can develop expansions for the square of this detectability as a function of the signal parameter, and that the lowest order expansions involve the Fisher information matrix for the problem of estimating the signal parameter. There are four basic methods we have considered for deriving such expansions. We compute these approximations to ideal-observer detectability for several cases. We compare these to the exact detectability values for these same cases, derived from results in previous work, to examine the usefulness of these approaches. The idea of using one parameterized probability density function is introduced in order to relate detection performance to estimation performance. Even without an analytical expression for ideal-observer detectability we are able to compute analytical forms for its derivatives in terms of the Fisher information matrix and similarly defined statistical moments. The results suggest that there is a connection between the performance of a system on signal-detection tasks and signal-estimation tasks.

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

Editors | D.P. Chakraborty, M.P. Eckstein |

Pages | 22-30 |

Number of pages | 9 |

Volume | 5 |

Edition | 26 |

DOIs | |

State | Published - 2004 |

Event | Medical Imaging 2004 - Image Perception, Observer Performance, and Technology Assessment - San Diego, CA, United States Duration: Feb 17 2004 → Feb 19 2004 |

### Other

Other | Medical Imaging 2004 - Image Perception, Observer Performance, and Technology Assessment |
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Country | United States |

City | San Diego, CA |

Period | 2/17/04 → 2/19/04 |

### Fingerprint

### Keywords

- Detectability
- Fisher information
- Hardware optimization
- Ideal observer
- Image quality
- Parameter estimation
- ROC analysis
- Signal detection

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(26 ed., Vol. 5, pp. 22-30). [02] https://doi.org/10.1117/12.534298

**Using fisher information to compute ideal-observer performance on detection tasks.** / Shen, Fangfang; Clarkson, Eric W.

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

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE.*26 edn, vol. 5, 02, pp. 22-30, Medical Imaging 2004 - Image Perception, Observer Performance, and Technology Assessment, San Diego, CA, United States, 2/17/04. https://doi.org/10.1117/12.534298

}

TY - GEN

T1 - Using fisher information to compute ideal-observer performance on detection tasks

AU - Shen, Fangfang

AU - Clarkson, Eric W

PY - 2004

Y1 - 2004

N2 - In medical imaging, signal detection is one of the most important tasks. A common way to evaluate the performance of an imaging system for a signal-detection task is to calculate the detectability of the ideal observer. Since the detectability of an ideal observer is not always easy to calculate, it is useful to have approximations for it. These approximations can also be used to check the bias of numerical computations of the ideal-observer detectability. For signal detection tasks, we usually have two probability densities for the data vector, the signal-absent density and the signal-present density. In this work, we use a single probability density with a variable scalar or vector parameter to represent the corresponding densities under the two hypotheses. The ideal-observer detectability is derived from the area under the receiver operating characteristic curve of the ideal observer for the given detection task. We have found that we can develop expansions for the square of this detectability as a function of the signal parameter, and that the lowest order expansions involve the Fisher information matrix for the problem of estimating the signal parameter. There are four basic methods we have considered for deriving such expansions. We compute these approximations to ideal-observer detectability for several cases. We compare these to the exact detectability values for these same cases, derived from results in previous work, to examine the usefulness of these approaches. The idea of using one parameterized probability density function is introduced in order to relate detection performance to estimation performance. Even without an analytical expression for ideal-observer detectability we are able to compute analytical forms for its derivatives in terms of the Fisher information matrix and similarly defined statistical moments. The results suggest that there is a connection between the performance of a system on signal-detection tasks and signal-estimation tasks.

AB - In medical imaging, signal detection is one of the most important tasks. A common way to evaluate the performance of an imaging system for a signal-detection task is to calculate the detectability of the ideal observer. Since the detectability of an ideal observer is not always easy to calculate, it is useful to have approximations for it. These approximations can also be used to check the bias of numerical computations of the ideal-observer detectability. For signal detection tasks, we usually have two probability densities for the data vector, the signal-absent density and the signal-present density. In this work, we use a single probability density with a variable scalar or vector parameter to represent the corresponding densities under the two hypotheses. The ideal-observer detectability is derived from the area under the receiver operating characteristic curve of the ideal observer for the given detection task. We have found that we can develop expansions for the square of this detectability as a function of the signal parameter, and that the lowest order expansions involve the Fisher information matrix for the problem of estimating the signal parameter. There are four basic methods we have considered for deriving such expansions. We compute these approximations to ideal-observer detectability for several cases. We compare these to the exact detectability values for these same cases, derived from results in previous work, to examine the usefulness of these approaches. The idea of using one parameterized probability density function is introduced in order to relate detection performance to estimation performance. Even without an analytical expression for ideal-observer detectability we are able to compute analytical forms for its derivatives in terms of the Fisher information matrix and similarly defined statistical moments. The results suggest that there is a connection between the performance of a system on signal-detection tasks and signal-estimation tasks.

KW - Detectability

KW - Fisher information

KW - Hardware optimization

KW - Ideal observer

KW - Image quality

KW - Parameter estimation

KW - ROC analysis

KW - Signal detection

UR - http://www.scopus.com/inward/record.url?scp=12144281721&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=12144281721&partnerID=8YFLogxK

U2 - 10.1117/12.534298

DO - 10.1117/12.534298

M3 - Conference contribution

VL - 5

SP - 22

EP - 30

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

A2 - Chakraborty, D.P.

A2 - Eckstein, M.P.

ER -