TY - GEN

T1 - Bias in hotelling observer performance computed from finite data

AU - Kupinski, Matthew A.

AU - Clarkson, Eric

AU - Hesterman, Jacob Y.

PY - 2007/10/15

Y1 - 2007/10/15

N2 - 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.

AB - 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.

KW - Bias

KW - Hotelling observer

KW - Image quality

UR - http://www.scopus.com/inward/record.url?scp=35148826936&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35148826936&partnerID=8YFLogxK

U2 - 10.1117/12.707800

DO - 10.1117/12.707800

M3 - Conference contribution

AN - SCOPUS:35148826936

SN - 0819466336

SN - 9780819466334

T3 - Progress in Biomedical Optics and Imaging - Proceedings of SPIE

BT - Medical Imaging 2007

T2 - Medical Imaging 2007: Image Perception, Observer Performance, and Technology Assessment

Y2 - 21 February 2007 through 22 February 2007

ER -