Image Reconstruction
Image reconstruction of 2-D PET data is accomplished by the same filtered
backprojection and iterative methods that have been described in detail
under SPECT in Chapter 12. In PET, the LORs in a sinogram are back-
projected by the Fourier method. In the iterative method, the projections
are estimated by determining the weighted sum of the activities in all pixels
along a LOR across the estimated image, and then compared with the mea-
sured projection.
The reconstruction of images from 3-D data is complicated by a very
large volume of data, especially in a multiring scanner. The direct applica-
tion of filtered backprojection and the iterative method to these data is
difficult, and so the 3-D sinogram data are rebinned into a set of 2-D
equivalent projections by assigning axially tilted LORS to transaxial planes
intersecting them at their axial midpoints. This method is called the single
slice rebinning method (SSRB). In another method, called the Fourier
rebinning (FORE) method, rebinning is performed by applying the Fourier
method to each oblique sinogram in the frequency domain. This method is
more accurate than the SSRB method because of the more accurate esti-
mate of the source axial location. After rebinning of 3-D data into 2-D data,
either the filtered backprojection or iterative method is applied.
Factors Affecting PET
As in gamma cameras, PET acquisition data are affected by photon atten-
uation, variation in detection efficiency of the detectors, scatter coinci-
dences, partial volume effect, and dead time. These factors are already
discussed under SPECT and therefore only subtle points pertinent to PET
data will be highlighted here. In addition, PET data are affected by some
unique factors such as random coincidence and parallax error (radial elon-
gation), which will be discussed below.
Normalization
There are 10,000 to 20,000 detectors arranged in blocks, and coupled to
several hundred PM tubes in modern PET scanners. Practically, as in
gamma cameras, the detection efficiency varies from detector pair to detec-
tor pair due to variation in the gain of PM tubes and location of the detec-
tor in the block, resulting in nonuniformity of the PET data. Data are
corrected for this factor by using what is called normalization. In normal-
ization of PET data, all detectors are exposed uniformly to a 511-keV
photon source (e.g.,^68 Ge source), without an object in the field of view, and
data are collected in the 2-D or 3-D mode. The normalization factors Fiare
calculated for individual pixels as
196 13. Positron Emission Tomography