Applications to Real Measured Data - Introduction to Imaging from Scattered Fields - page 136

Figures 9.22d and 9.22e show the reconstructions obtained using a modi-
fied gradient method (MGM) for the inversion of the scattered field data in
conjunction with an adaptive multiscale approach based on spline pyramids
to improve image quality (Baussard, 2005). Figure 9.22d shows the recon-
struction using MGM by itself. Again the quality of image reconstruction
seems poor, as the boundaries of inner and outer cylinders are not distin-
guishable. Figure 9.22e shows reconstruction using MGM with an adaptive
multiscale approach (Baussard, 2005). This method seems to do a decent job
in recovering permittivities of the cylinders. The reported permittivities for
the outer cylinder and the inner cylinder are ε r ≈ 2.5 and ε r ≈ 1.68, respec-
tively. The reconstruction obtained with this approach has shown good
results but at the cost of 15% more computation time as compared to MGM.
Figure 9.22f,g shows the reconstruction of FoamDielInt by a technique,
which combined diagonal tensor approximation (DTA), and CSI (Abubakar
et al., 2005). The reconstructions from this method seem by far the best, but
again it uses an iterative approach, which is computationally expensive, and
there is no guarantee of the convergence of the algorithm to a solution, right
or wrong. Figure 9.22 h shows reconstruction from another iterative method
based on a Bayesian inversion method. The quality of this reconstruction
method seems poor in a sense that it not only fails to retrieve the correct
dimensions of the cylinders but also gives a poor estimate of relative permit-
tivity. The reconstructions shown in Figures 9.22i and 9.22j are obtained by
using an iterative multiscaling approach (IMSA), which exploits the scattered
field data through a multistep reconstruction procedure (Donelli et al., 2005).
Figure 9.22i shows the reconstruction when the incident wave is modeled as
a plane wave and Figure 9.22j shows the reconstruction when the incident
wave is modeled as a line source. Figure 9.22 k shows an image estimate
using another iterative approach (Litman, 2005). This approach seems to do
a good job in recovering the shape of the object but it fails to recover any
quantitative information about the object. Figure 9.22l shows a reconstruc-
tion using the cepstral filtering method (Shahid, 2009). Considering the fact
that it is a noniterative low computational cost algorithm, the reconstruction
not only gives a good estimate of the object's geometry but also gives a mean-
ingful recovery of relative permittivities. The reconstruction comparison for
FoamDielExt, FoamTwinDiel, and FoamMetExt are shown in Figures 9.23
through 9.25, respectively.
Figure 9.23 shows the reconstructions of FoamDielExt from various meth-
ods as previously. Again most of the methods seem to fail to do a reason-
able job in reconstructing FoamDielExt except reconstructions shown in
Figures 9.23f and 9.23 g, which was done using a combination of DTI and
CSI (Abubakar et al., 2005). Figure 9.23h, which was reconstructed using a
Bayesian inversion method (Feron et al., 2005), seems to give a good estimate
of shape but seems to lacks quantitative accuracy. Figures 9.23i and 9.23j,
which are based on IMSA (Donelli et al. 2005), show artifacts in reconstruc-
tion. The reconstruction shown in Figure 9.23e is based on MGM along with
a multiscale approach (Baussard, 2005). The quality of reconstruction seems
good in a sense that it has not only recovered shape but also relative permittiv-
ity. The only downside is that it is an iterative process and it takes 15% more
iterations as compared to MGM. The reconstruction from the cepstral method,
Figure 9.23l, seems to have done a reasonable job in recovering permittivity