Bias in roj estimators and an unbiased solution

Meredith Kathryn Whitaker, Eric W Clarkson, Harrison H Barrett

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and otTers a substantial improvement, as measured by the ensemble-mean squared error (EMSE), when compared to using voxel values from a maximum-likelihood expectationmaximization (MLEM) reconstructed ROI. The scanning-linear estimator is derived as a special case of maximum-likelihood (ML) techniques with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise, and variability in the signal's activity. The resulting estimate of the signal activity is an unbiased estimator: the average estimate equals the true value. By contrast, algorithms that operate on reconstructed data are subject to unpredictable bias arising from the null functions of the imaging system and the object. Using visual inspetion of reconstructed data to select an ROI is tantamoun to estimating a location and size of the signal. general, this procedure would less than ideal, but we remove this source of error by estimating the activity of a spherical signal whose radius and centroid are known. The signal shape and location fully specify a binary ROI template in object space. Although the scanning-linear method can be generalized to more complicated estimation tasks, we will demonstrate its use for estimating only signal amplitude. Noisy projection data are realistically emulated using measured calibration data from the multi-module multiresolution (M 3R) small-animal SPECT imaging system. The scanning-linear estimate of signal activity is computed for 800 image samples. The same set of images are reconstructed using the MLEM algorithm (80 iterations), and the mean as well as the maximum value within the ROI is calculated.

Original languageEnglish (US)
Title of host publication2008 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2008
Number of pages3
StatePublished - 2008
Event2008 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2008 - Dresden, Germany
Duration: Oct 19 2008Oct 25 2008

Publication series

NameIEEE Nuclear Science Symposium Conference Record
ISSN (Print)1095-7863


Other2008 IEEE Nuclear Science Symposium Conference Record, NSS/MIC 2008


  • Assessment of image quality
  • Terms-Estimation

ASJC Scopus subject areas

  • Radiation
  • Nuclear and High Energy Physics
  • Radiology Nuclear Medicine and imaging


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