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

E. Clarkson, A. R. Pineda, H. H. Barrett

Research output: Contribution to journalConference articlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)339-349
Number of pages11
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2001
EventMedical Imaging 2001: Physics of Medical Imaging - San Diego, CA, United States
Duration: Feb 18 2001Feb 20 2001


  • Detectability
  • Digital radiography
  • Image quality
  • SNR

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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