Many commercial software packages are available offering a variety of
choices for filters and cut-off values. The selection of a cut-off value is
important such that noise is reduced and image detail is preserved. Reduc-
ing a cut-off value will increase smoothing but will curtail low-frequency
patient data and thus degrade image contrast particularly in smaller lesions.
No filter is perfect and, therefore, the design, acceptance, and implementa-
tion of a filter are normally done by trial and error with the ultimate result
of clinical utility.
As already mentioned, filtered backprojection was originally applied only
to transverse slices from which vertical and horizontal long axis slices are
constructed. Filtering between the adjacent slices is not performed, and this
results in distortion of the image in planes other than the transverse plane.
With algorithms available in current SPECT systems, filtering can be
applied to slices perpendicular to transverse planes or in any plane through
the 3-D volume of an object. This process is called volume smoothing.
However, because of increased popularity of iterative methods described
below, the 3-D volume smoothing is not widely applied.
Iterative Reconstruction
The basic principle of iterative reconstruction involves a comparison
between the measured image and an estimated image that is repeated until
a satisfactory agreement is achieved. In practice, an initial estimate is made
of individual pixels in a projection of a reconstruction matrix of the same
size as that of the acquisition matrix, and the projection is then compared
with that of the measured image. If the estimated pixel values in the pro-
jection are smaller or greater than the measure values, then each pixel value
is adjusted in relation to other pixels in the projection to obtain an updated
estimated projection, which is then compared with the measured projec-
tion. This process is repeated until a satisfactory agreement is obtained
between the estimated and actual images. The schematic concept of itera-
tive reconstruction is illustrated in Figure 12.12. The method makes many
iterations requiring long computation time and thus discouraging its
general use in image reconstruction until recently. However, with the avail-
ability of faster computers nowadays, this method is gaining popularity in
image reconstruction, particularly in PET imaging.
Initially a uniform image is arbitrarily estimated for comparison (e.g., all
pixel counts equal to 0, 1, or a mean value). The image is then unfolded into
a set of projections by a process called forward projectionas opposed to
backprojection. It is accomplished by determining the weighted sum of the
activities in all pixels in the projection across the estimated image. From
Figure 12.13, a projection qiin the estimated image is given by
qaCiij (12.4)
jN
= j
=∑
1166 12. Single Photon Emission Computed Tomography