Fully 3-D PET reconstruction with system matrix derived from point source measurements

The quality of images reconstructed by statistical iterative methods depends on an accurate model of the relationship between image space and projection space through the system matrix. The elements of the system matrix for the clinical Hi-Rez scanner were derived by processing the data measured for a point source at different positions in a portion of the field of view. These measured data included axial compression and azimuthal interleaving of adjacent projections. Measured data were corrected for crystal and geometrical efficiency. Then, a whole system matrix was derived by processing the responses in projection space. Such responses included both geometrical and detection physics components of the system matrix. The response was parameterized to correct for point source location and to smooth for projection noise. The model also accounts for axial compression (span) used on the scanner. The forward projector for iterative reconstruction was constructed using the estimated response parameters. This paper extends our previous work to fully three-dimensional. Experimental data were used to compare images reconstructed by the standard iterative reconstruction software and the one modeling the response function. The results showed that the modeling of the response function improves both spatial resolution and noise properties.