Bias in Hotelling observer performance computed from finite data

Matthew A. Kupinski; Eric Clarkson; Jacob Y. Hesterman

doi:10.1117/12.707800

20 March 2007 Bias in Hotelling observer performance computed from finite data

Matthew A. Kupinski, Eric Clarkson, Jacob Y. Hesterman

Author Affiliations +

Proceedings Volume 6515, Medical Imaging 2007: Image Perception, Observer Performance, and Technology Assessment; 65150S (2007) https://doi.org/10.1117/12.707800
Event: Medical Imaging, 2007, San Diego, CA, United States

Abstract

An observer performing a detection task analyzes an image and produces a single number, a test statistic, for that image. This test statistic represents the observers "confidence" that a signal (e.g., a tumor) is present. The linear observer that maximizes the test-statistic SNR is known as the Hotelling observer. Generally, computation of the Hotelling SNR, or Hotelling trace, requires the inverse of a large covariance matrix. Recent developments have resulted in methods for the estimation and inversion of these large covariance matrices with relatively small numbers of images. The estimation and inversion of these matrices is made possible by a covariance matrix decomposition that splits the full covariance matrix into an average detector-noise component and a background-variability component. Because the average detector-noise component is often diagonal and/or easily estimated, a full-rank, invertible covariance matrix can be produced with few images. We have studied the bias of estimates of the Hotelling trace using this decomposition for high-detector-noise and low-detector noise situations. In extremely low-noise situations, this covariance decomposition may result in a significant bias. We will present a theoretical evaluation of the Hotelling-trace bias, as well as extensive simulation studies.

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Matthew A. Kupinski, Eric Clarkson, and Jacob Y. Hesterman "Bias in Hotelling observer performance computed from finite data", Proc. SPIE 6515, Medical Imaging 2007: Image Perception, Observer Performance, and Technology Assessment, 65150S (20 March 2007); https://doi.org/10.1117/12.707800

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