Normalization for 3D PET with a low-scatter planar source and measured geometric factors

For 3D PET normalization methods, a balance must be struck between statistical accuracy and individual detector or line-of-response (LOR) fidelity. Methods with potentially the best LOR accuracy tend to be statistically poor, while techniques to improve the statistical quality tend to reduce the individual detector fidelity. We have developed and implemented a 3D PET normalization method for our ECAT 953B scanner (Siemens/CTI) that determines the detector normalization factors (NFs) as a product of a four-dimensional matrix of measured geometric factors (GFs) and single detector efficiency factors (epsilon). The effects of various alterations to the algorithm on the accuracy of the normalization have been examined through the impact on reconstructed images. An accurate set of GFs is crucial, as inaccurate NFs can result if LORs with similar but not identical geometric symmetries are grouped together. The general method can be extended to other tomographs, although the dimensionality of a GF matrix may be scanner-specific; the key is to determine the optimal number of dimensions in the GF matrix. The GFs for our scanner are specified by: (i) the two detector rings for each LOR; (ii) the radial distance of the LOR from the tomograph centre; and (iii) the positions within the detector block of the two crystals defining the LOR. Some residual radial non-uniformities are present in all the NF variations we examined. For the NF method presented here, the radial non-uniformities are attributed to the interaction between object-dependent scatter and normalization. Results indicate that this non-uniformity is detectable for scans with as few as 13 million total counts.