Image Processing Reference

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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

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