An approximation formula for the variance of PET region-of-interest values

An approximation formula for the variance of positron emission tomography (PET) region-of-interest (ROI) values has been developed, implemented, and evaluated. This formula does not require access to the original projection data and is therefore convenient for routine use. The formula was derived by applying successive approximations to the filtered-backprojection reconstruction algorithm. ROI variance is estimated from the product of mean pixel variance within the region and a term accounting for the intercorrelation of all pixel pairs inside the region. The formula accounts for radioactivity distribution, attenuation, randoms, scatter, deadtime, detector normalization, scan length, decay, and reconstruction filter. The algorithm was tested by comparison to the exact ROI variance as calculated with Huesman´s algorithm. Tests with scan data from phantoms, animals, and humans obtained on the Scanditronix PC2048-15B tomograph showed the approximation formula to be accurate to within ±10%