Biomedical Engineering Reference
In-Depth Information
FIGURE 4.1 (continued)
(g) The convolved object sampled at regular intervals with spacing
. The sampled values
lie exactly on the convolved object profile. (h) Selection of slices at spacing
d
d
results in
. Frequencies outside this range
get folded back, resulting in aliasing (shaded regions). Note that the frequency scale (hori-
zontal axis) has been expanded for clarity. (i) Resampling the slices from the originally
acquired slice positions results in local signal intensity errors (The calculated sample values
no longer lie on the convolved object profile). (j) The process of resampling the slices alters
the frequency spectrum because the aliased frequencies interact with the interpolation
algorithm. (Note that the spectrum now extends beyond 2
sampling of the spectrum in (f) up to a frequency of 2
d
d
. The horizontal frequency
Noll
()
scale is the same as in (h)). (Adapted from
with thanks to Dr. C. Triantyfallou).
are being deliberately acquired for the purposes of image registration, it may
be valuable to monitor spatial coverage and take steps to fill in sparsely sam-
pled regions. When insufficient sampling has been achieved, this can be
detected and the final results judged accordingly. A feature of sampling in the
real object space, as in slice selection, is that local undersampling results in
local vulnerability to intensity errors upon reslicing.
Slice overlap naturally comes at a price, which may be time and
or dose for
CT and ultrasound but is further complicated by saturation effects in MRI.
2
Conventional multislice MRI is not obtained with overlapping slices and so is
highly vulnerable to data corruption due to aliasing when resliced (Figure 4.2).
However, true 3D MRI data, in which Fourier encoding is applied in all three
spatial directions, are intrinsically adequately sampled, so are amenable to
reslicing without aliasing errors.
