Analytical approximations to the Hotelling trace for digital x-ray detectors

Eric Clarkson; Angel R. Pineda; Harrison H. Barrett

doi:10.1117/12.430932

28 June 2001 Analytical approximations to the Hotelling trace for digital x-ray detectors

Eric Clarkson; Angel R. Pineda; Harrison H. Barrett

Author Affiliations +

Proceedings Volume 4320, Medical Imaging 2001: Physics of Medical Imaging; (2001) https://doi.org/10.1117/12.430932
Event: Medical Imaging 2001, 2001, San Diego, CA, United States

Abstract

The Hotelling trace is the signal-to-noise ratio for the ideal linear observer in a detection task. We provide an analytical approximation for this figure of merit when the signal is known exactly and the background is generated by a stationary random process, and the imaging system is an ideal digital x-ray detector. This approximation is based on assuming that the detector is infinite in extent. We test this approximation for finite-size detectors by comparing it to exact calculations using matrix inversion of the data covariance matrix. After verifying the validity of the approximation under a variety of circumstances, we use it to generate plots of the Hotelling trace as a function of pairs of parameters of the system, the signal and the background.

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Eric Clarkson, Angel R. Pineda, Harrison H. Barrett, "Analytical approximations to the Hotelling trace for digital x-ray detectors", Proc. SPIE 4320, Medical Imaging 2001: Physics of Medical Imaging, (28 June 2001); doi: 10.1117/12.430932; https://doi.org/10.1117/12.430932

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