### Abstract

In medical imaging, signal detection is one of the most important tasks. It is especially important to study detection tasks with signal location uncertainty. One way to evaluate system performance on such tasks is to compute the area under the localization-receiver operating characteristic (LROC) curve. In an LROC study, detecting a signal includes two steps. The first step is to compute a test statistic to determine whether the signal is present or absent. If the signal is present, the second step is to identify the location of the signal. We use the test statistic which maximizes the area under the LROC curve (ALROC). We attempt to capture the distribution of this ideal LROC test statistic with signal-absent data using the extreme value distribution. Some simulated test statistics are shown along with extreme value distributions to illustrate how well our approximation captures the characteristics of the ideal LROC test statistic. We further derive an approximation to the ideal ALROC using the extreme value distribution and compare it to the direct simulation of the ALROC. Using a different approach by defining a parameterized probability density function of the data, we are able to derive another approximation to the ideal ALROC for weak signals from a power series expansion in signal amplitude.

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

Title of host publication | Progress in Biomedical Optics and Imaging - Proceedings of SPIE |

Volume | 6515 |

DOIs | |

State | Published - 2007 |

Event | Medical Imaging 2007: Image Perception, Observer Performance, and Technology Assessment - San Diego, CA, United States Duration: Feb 21 2007 → Feb 22 2007 |

### Other

Other | Medical Imaging 2007: Image Perception, Observer Performance, and Technology Assessment |
---|---|

Country | United States |

City | San Diego, CA |

Period | 2/21/07 → 2/22/07 |

### Fingerprint

### Keywords

- ALROC
- Extreme value distribution
- Location uncertainty
- LROC
- ROC
- Signal detection
- Test statistic

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE*(Vol. 6515). [651510] https://doi.org/10.1117/12.708666

**Approximating the test statistic distribution and ALROC in signal-detection tasks with signal location uncertainty.** / Shen, Fangfang; Clarkson, Eric W.

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

*Progress in Biomedical Optics and Imaging - Proceedings of SPIE.*vol. 6515, 651510, Medical Imaging 2007: Image Perception, Observer Performance, and Technology Assessment, San Diego, CA, United States, 2/21/07. https://doi.org/10.1117/12.708666

}

TY - GEN

T1 - Approximating the test statistic distribution and ALROC in signal-detection tasks with signal location uncertainty

AU - Shen, Fangfang

AU - Clarkson, Eric W

PY - 2007

Y1 - 2007

N2 - In medical imaging, signal detection is one of the most important tasks. It is especially important to study detection tasks with signal location uncertainty. One way to evaluate system performance on such tasks is to compute the area under the localization-receiver operating characteristic (LROC) curve. In an LROC study, detecting a signal includes two steps. The first step is to compute a test statistic to determine whether the signal is present or absent. If the signal is present, the second step is to identify the location of the signal. We use the test statistic which maximizes the area under the LROC curve (ALROC). We attempt to capture the distribution of this ideal LROC test statistic with signal-absent data using the extreme value distribution. Some simulated test statistics are shown along with extreme value distributions to illustrate how well our approximation captures the characteristics of the ideal LROC test statistic. We further derive an approximation to the ideal ALROC using the extreme value distribution and compare it to the direct simulation of the ALROC. Using a different approach by defining a parameterized probability density function of the data, we are able to derive another approximation to the ideal ALROC for weak signals from a power series expansion in signal amplitude.

AB - In medical imaging, signal detection is one of the most important tasks. It is especially important to study detection tasks with signal location uncertainty. One way to evaluate system performance on such tasks is to compute the area under the localization-receiver operating characteristic (LROC) curve. In an LROC study, detecting a signal includes two steps. The first step is to compute a test statistic to determine whether the signal is present or absent. If the signal is present, the second step is to identify the location of the signal. We use the test statistic which maximizes the area under the LROC curve (ALROC). We attempt to capture the distribution of this ideal LROC test statistic with signal-absent data using the extreme value distribution. Some simulated test statistics are shown along with extreme value distributions to illustrate how well our approximation captures the characteristics of the ideal LROC test statistic. We further derive an approximation to the ideal ALROC using the extreme value distribution and compare it to the direct simulation of the ALROC. Using a different approach by defining a parameterized probability density function of the data, we are able to derive another approximation to the ideal ALROC for weak signals from a power series expansion in signal amplitude.

KW - ALROC

KW - Extreme value distribution

KW - Location uncertainty

KW - LROC

KW - ROC

KW - Signal detection

KW - Test statistic

UR - http://www.scopus.com/inward/record.url?scp=35148897780&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35148897780&partnerID=8YFLogxK

U2 - 10.1117/12.708666

DO - 10.1117/12.708666

M3 - Conference contribution

AN - SCOPUS:35148897780

SN - 0819466336

SN - 9780819466334

VL - 6515

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

ER -