Image Processing Reference
community as most of the algorithms applied are typically based on the first
Born approximation, and clearly the image obtained using the Born approxi-
mation shows poor reconstruction (Figure 9.2b). When an incident plane wave
impinges on IPS008, it gets diffracted at the boundary of the larger cylinder.
As a result, the wave that is incident on the smaller cylinder can be inter-
preted as a convergent wave front. This constitutes a serious violation of the
first-order Born approximation, which assumes the incident field to pass the
target essentially unperturbed, as a result of which we see artifacts in the
reconstruction as shown in Figure 9.2b. Figure 9.2c shows the reconstruc-
tion obtained using the cepstral method discussed earlier in this topic. The
image of Figure 9.2c looks much better as compared with an estimate using
the Born approximation. The step-by-step process of recovering a scattering
object using cepstral filtering method is shown in Figure 9.3. It not only gives
an improved estimate of the shape of object but also provides a good approxi-
mation of the permittivity distribution. The cepstral filtering method does a
good job in recovering the dimensions of cylinders; however, the recovered
inner cylinder is not tangent to the external one as it should be.
It is suspected that this difference in the position of the inner cylinder is
due to the limited data coverage. It will be shown that the spectral estimation
technique, prior discrete Fourier transform (PDFT), can help in resolving this
Figure 9.4 shows the comparison of reconstructed IPS008 object from vari-
ous inverse scattering groups published in IEEE Antennas and Propagation
Magazine (Belkebir and Saillard, 2001; Byrne and Fitzgerald, 1984; Estatico
et al., 2005) and a minimum phase-based reconstruction.
Further improvements could possibly be realized by applying the PDFT
techniques described in Chapter 7. An example of the effects of this technique
in conjunction with cepstral filtering and apparent improvements in terms of
dimensions for the IPS008 data is illustrated in Figure 9.5.
The IPS010 target consists of a dielectric wedge made of Plexiglass with rela-
tive permittivity ε r ≈ 2.25. The IPS010 has also proven to be a very challenging
object for participating groups to image due to its high permittivity and sharp
shape features. Figure 9.6 shows the Born reconstruction and cepstral recon-
struction for this image data.
Combination of the wedge shape and high permittivity has made this object
very difficult to image. The cepstral method does a reasonable job in recover-
ing the quantitative description of IPS010; however, the shape estimation is
still poor both in the Born and cepstral methods. One reason for this poor
shape could be the insufficient sampling rate. The same number of illumina-
tion angles, which are used to reconstruct simple cylindrical objects, may not
be sufficient to reconstruct a wedge-shaped object with sharp features.
As before, the PDFT algorithm was applied to IPS010 to improve recon-
struction quality. It is important to have some knowledge about the object,
such as size, shape and location, in order to distinguish between target and
artifacts. Unwanted signal components can be minimized or eliminated by
carefully choosing a prior to encompass V as tightly as one can reasonably
estimate without cutting in to the actual dimensions of V . Actually, if one did,
the energy of the PDFT estimate would become very large and one can use
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