Biomedical Engineering Reference
In-Depth Information
where
F
1
[ ] represents a one-dimensional Fourier transform. It can be shown that the trans-
form of each projection forms a radial line in
(
,
), and therefore
(
,
) can be determined
F
u
v
F
u
v
by taking projections at many angles and taking these transforms. When
) is completely
described, the reconstructed image can be found by taking the inverse Fourier transform to
obtain
(
,
F
u
v
).
The image reconstruction method used by most modern CAT scanners is the filtered back-
projection reconstruction method. In this method, attenuation projection data for a given ray
or scan angle are convolved with a spatial filter function either in the Fourier domain or by
direct spatial convolution. The filtered data are then back-projected along the same line, using
the measured value for each point along the line, as shown in Figure 15.16. The total back-
projected image is made by summing the contributions from all scan angles. Depending on
the filter technique, the image is obtained directly after back-projection summation or via
the inverse Fourier transform of the back-projected image.
It should be obvious by now that compared to early head and body scanners, current
models process information faster, use energy more efficiently, are more sensitive to differ-
ences in tissue density, have finer spatial resolution, and are less susceptible to artifacts. CT
scanners may be compared with one another by considering the following ten factors:
f
(
x
,
y
1.
Gantry design
, which affects scan speed, patient processing time, and cost-effectiveness
2.
Aperture size
, which determines the maximum size of the patient along with the weight-
carrying capacity of the couch
3.
The type of x-ray source
, which affects the patient radiation dose and the overall life of the
scanning device
4.
X-ray fan beam angle and scan field
, which affects resolution
5.
The slice thickness
, as well as the number of pulses and the angular rotation of the source,
which are important in determining resolution
, which are critical parameters in image quality
6.
The number and types of detectors
, which is important in assessing system capability and
7.
The type of minicomputer employed
flexibility
8.
The type of data-handling routines
available with the system, which are important user
and reliability considerations
9.
The storage capacity
of the system, which is important in ascertaining the accessibility of
the stored data
10.
Upgradeability and connectivity
—that is, they should be capable of modular upgradeability
and should communicate to any available network
FIGURE 15.16
The results obtained with a simple back-projection algorithm.
