Biomedical Engineering Reference
In-Depth Information
(a) Signal
(b)
Tissue
fraction
(c) Spill-over
(d) Spill-over and TF
(TF)
FIGURE 7.12: Partial volume effects for a 1D signal. Tics on x-axis denote
sampling intervals. (a) Input signal. (b) Due to tissue fraction the signal is an
average of the intensities within the respective sampling area. (c) Spill-over
causes part of the signal intensity to appear outside of the area of the true
signal. (d) Combined effect of tissue fraction and spill-over. The input signal
is plotted as a dashed line in (b){(d) for orientation.
spatial resolution of imaging systems, e.g., the size and distance of detector
crystals [51]. Besides physical limitations of PET scanners, the process of re-
construction contributes to the PVE as well.
The spill-over eect aects a voxel's intensity twofold: rst, a voxel dis-
tributes part of its own signal to the surrounding region. Secondly, the voxel
gets signal intensity from its neighbors. The following equation formalizes this
relationship:
I(x) = I
u
(x) I
out
(
x
) + I
in
(
x
) :
(7.25)
The intensity of a voxel x in the reconstructed PET image I is composed of
the actual intensity I
u
, a spill-out I
out
of intensity into the neighborhood
x
and a spill-in I
in
from the neighboring voxels. Thus, the observed intensities
are a mixture of the true intensities. Without knowledge of the exact amount
of spill-in and spill-out it is not possible to reconstruct the true signal of a
voxel. Many existing correction methods try to estimate the unknowns I
in
and
I
out
in Equation (7.25) to compute the true signal.
Figure 7.12 shows the effects of tissue fraction and spill-over for a 1D
signal (Figure 7.12(a)): Tissue fraction causes an averaging of all intensities
within each sampling bin (Figure 7.12(b)). Spill-over causes part of the inten-
sity to be visible outside of the area of the original signal (Figure 7.12(c)).
The combination of both effects is illustrated in Figure 7.12(d).
7.5.2 Correction methods
In the following, methods used for partial volume correction (PVC) are
discussed and we introduce a few representative algorithms. PVC is not yet
commonly used in clinical environments, despite the great effort spent on PVC
research in recent years. Yet, the importance of PVC for quantification has
been shown [3, 65].
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