This approximate algorithm  is based on the assumption that each measured oblique LOR only traverses a single transaxial section within the support of the tracer distribution. Referring to the third argument of f in Eq. (54), this assumption amounts to neglecting the product RF tan 9, where RF , the radius of the FOV, is the maximum value of the variable t'. Using this approximation, Eq. (65) can be extended to preb (S,Q,Z) - ps (S,0,£= Z,d = 0) (66)
and by averaging all available estimates, SSRB defines the rebinned sinograms by
is the maximum axial aperture for an LOR at a distance s from the axis in slice z. The algorithm is exact for tracer distributions which are linear in Z, of the type f(x,y, z) = a(x,y) + zb(x,y). For realistic distributions, the accuracy of the approximation will decrease with increasing RF and 0max. Axial blurring and transaxial distortions increasing with the distance from the axis of the scanner are the main symptoms of the SSRB approximation.
The discrete implementation of the SSRB algorithm is simply the extension of the technique described in the multi-slice 2D data section (above) to build 2D data with a multi-ring scanner operated in 2D mode, with d2Dmax replaced by a larger value dmax. The choice of dmax entails a compromise between the systematic errors (which increase with dmax) and the reconstructed image variance (which increases with decreasing dmax).
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