Biomedical Engineering Reference
In-Depth Information
the
convolution-backprojection
in the spatial domain. The implementation of
FBP involves four major steps:
1. Take the one-dimensional Fourier transform for each projection.
2. Multiply the resultant transformation by the frequency filter.
3. Compute the inverse Fourier transform of the filtered projection.
4. Back-project the data for each projection angle.
However, the side effect of the ramp filtering using equation (2.9) is that
high-frequency components in the image that tend to be dominated by statis-
tical noise are amplified [32]. The detectability of lesion or tumor is therefore
severely hampered by this noise amplification during reconstruction by FBP,
particularly when the scan duration is short or the number of counts recorded is
low. To obtain better image quality, it is desirable to attenuate the high-frequency
components by using some window functions, such as the Shepp-Logan or
the Hann windows, which modify the shape of the ramp filter at higher fre-
quencies [33]. Unfortunately, the attenuation of higher frequencies in filtering
process will degrade the spatial resolution of the reconstructed images, and we
will briefly discuss it in Section 2.13.
2.10.2 Iterative Reconstruction
Alternatively, emission tomographic images can be reconstructed with iterative
statistical-based reconstruction methods. Instead of using an analytical solu-
tion to produce an image of radioactivity distribution from its projection data,
iterative reconstruction makes a series of image estimates, compares forward-
projections of these image estimates with the measured projection data and
refines the image estimates by optimizing an objective function iteratively until
a satisfactory result is obtained. Improved reconstruction compared with FBP
can be achieved using these approaches, because they allow accurate modeling
of statistical fluctuation (noise) in emission and transmission data and other
physical processes [34, 35]. In addition, appropriate constraints (e.g. nonnega-
tivity) and
a priori
information about the object (e.g. anatomic boundaries) can
be incorporated into the reconstruction process so that better image quality can
be achieved [36, 37].
