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New statistical models for randoms-precorrected PET scans

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1230)

Abstract

PET measurements are usually precorrected for accidental coincidence events by real-time subtraction of the delayed window coincidences. Randoms subtraction compensates in mean for accidental coincidences but destroys the Poisson statistics. We propose and analyze two new approximations to the exact log-likelihood of the precorrected measurements, one based on a “shifted Poisson” model, the other based on saddle-point approximations to the measurement probability mass function (pmf). The methods apply to both emission and transmission tomography; however in this paper we focus on transmission tomography. We compare the new models to conventional data-weighted least squares (WLS) and conventional maximum likelihood (based on the ordinary Poisson (OP) model) using simulations and analytic approximations. The results demonstrate that the proposed methods avoid the systematic bias of the WLS method, and lead to significantly lower variance than the conventional OP method. The saddle-point method provides a more accurate approximation to the exact log-likelihood than the WLS, OP and shifted Poisson alternatives. However, the simpler shifted Poisson method yielded comparable bias-variance performance in the simulations. The new methods offer improved image reconstruction in PET through more realistic statistical modeling, yet with negligible increase in computation over the conventional OP method.

Keywords

  • Left Half Plane
  • Coincidence Event
  • Accidental Coincidence
  • Transmission Tomography
  • Independent Poisson Random Variable

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported in part by NIH grants CA-60711 and CA-54362.

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© 1997 Springer-Verlag Berlin Heidelberg

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Yavuz, M., Fessler, J.A. (1997). New statistical models for randoms-precorrected PET scans. In: Duncan, J., Gindi, G. (eds) Information Processing in Medical Imaging. IPMI 1997. Lecture Notes in Computer Science, vol 1230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63046-5_15

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  • DOI: https://doi.org/10.1007/3-540-63046-5_15

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