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.

Citation Download Citation

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