An analytical approach to quantify uniformity artifacts for circular and noncircular detector motion in single photon emission computed tomography imaging

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Abstract
Uniformity artifacts in rotating gamma camera tomography will result if there are errors in the correction factors which are routinely calculated from a static uniformity flood image. The accuracy of the correction factors is a function of the statistics in the collected flood image. Since the factors are applied to each projection view, an error in a correction factor will propagate as a projection error at the same pixel location for each view. For circular detector motion, the error in each projection is reconstructed as a ring whose maximum amplitude varies approximately inversely proportional to the square root of the distance of the projection error from the center of rotation. For noncircular detector motion the artifacts are not rings but are more complicated geometric curves. Simulations show that statistical fluctuations in the reconstructed image will mask the uniformity artifacts provided the correction flood satisfies minimum count requirements. An analytical expression is derived for the percent root‐mean‐square (% rms) error in the reconstruction and is compared with the percent relative amplitude error (% RAE) of the reconstructed artifacts in order to obtain expressions for uniformity flood counting statistics. For an elliptical source distribution with total counts equal to CT, the uniformity statistics required to reconstruct elliptical disks is inversely proportional to the square root of the area: Ū≥KCT/area1/2. The constant K depends on the filter function and type of detector motion.