25 April 1997 Algorithm to reduce the complexity of local statistics computation for PET images
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Abstract
The evaluation of the local statistical noise in a region of interest (ROI) of reconstructed positron emission tomography (PET) images is necessary for quantitative activity studies. Huesman provided an exact but highly complicated way to calculate covariances of ROIs in PET images. To reduce the computational complexity in Huesman's method, various approximate formulae for covariance estimation have been developed, but these techniques have limited accuracies. We propose a method which accelerates the covariance calculation and also secures the accuracy. This method exploits the circulant property of the coefficient vector of the convolution filter used in filtered backprojection (FBP). The covariance calculation is significantly accelerated by using a table look-up followed by multiplications with the corrected projection data. Results show that, for equal-weighted linear interpolation FBP, the number of computation required for this new covariance computation is about half of that of Huesman's method.
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Chung-Chieh Jack Huang, Xiaoli Yu, J. Zeng, James R. Bading, Peter S. Conti, "Algorithm to reduce the complexity of local statistics computation for PET images", Proc. SPIE 3034, Medical Imaging 1997: Image Processing, (25 April 1997); doi: 10.1117/12.274090; https://doi.org/10.1117/12.274090
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