Image Processing Reference

In-Depth Information

defining its actual diameter. On the right we see, to the same scale, an image

of a weaker object (permittivity = 1.1) for which the Born approximation is not

good, but not necessarily that bad either. The detrimental effect on the qual-

ity of the reconstructed image is evident by the degree to which the periodic

features arise in the image. This degradation is due to the data truncation

in
k
-space. As the permittivity of the cylinder increases, we pass through a

series of resonances and for each of these, there is a strong field enhance-

ment inside the cylinder and the measured scattered field in the far field will

reflect this. We see that for those situations, the Born reconstructions are quite

good. This is evident by matching the ε
r
for maximum scattering in Figures

6.3 and 6.4 with the corresponding reconstructions shown in Tables 6.11 and

6.12, respectively. What is worth noting about these sets of reconstructions is

to see how, at resonance, the far-field measurements seemingly correspond

to a relatively weak scatterer but with a larger diameter. Consider for exam-

ple the reconstructions in Table 6.12 for ε
r
= 1.4 compared with ε
r
= 2.1; both

appear reasonably uniform inside the cylinder but neither of them is the cor-

rect diameter. Not unsurprisingly, the relative distortion (increase) in size is

proportional to the increased radar cross section. The problem of nonscatter-

ing and scattering structures and the so-called “bound states” that can store

energy in a scattering object at certain frequencies has long been recognized

as an inherent ambiguity or lack of uniqueness one must accept in inverse

scattering problems. Of course, changing the frequency of illumination can

resolve such ambiguities but not entirely since the material properties such as

permittivity will be wavelength-dependent.

ReFeRenCeS

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multiplicative regularized contrast source inversion method on TM & TE

polarized experimental Fresnel data.
Inverse Problems, 21
, 5-13.

Baussard, A. 2005. Inversion of multi-frequency experimental data using an

adaptive multiscale approach.
Inverse Problems, 21
, 15-31.

Belkebir, K. and Saillard, M. 2001. Special section: Testing inversion algorithms

against experimental data.
Inverse Problems, 17
, 1565-1571.

Belkebir, K. and Saillard, M. 2005. Special section on testing inversion algo-

rithms against experimental data: Inhomogeneous targets,
Inverse

Problems
, 21, S1-S3.

Byrne, C. L. and Fitzgerald, R. M. 1984. Spectral estimators that extend the

maximum entropy and maximum likelihood methods.
SIAM Journal of

Applied Mathematics, 44
, 425-442.

Donelli, M., Franceschini, D., Massa, A., Pastorino, M., and Zanetti, A. 2005.

Multi-resolution iterative inversion of real inhomogeneous targets.
Inverse

Problems, 21
, 51-63.

Estatico, C., Bozza, G., Massa, A., Pastorino, M., and Randazzo, A. 2005. A

two-step iterative inexact-Newton method for electromagnetic imaging of

dielectric structures from real data.
Inverse Problems, 21
, 81-94.

Feron, O., Duchene, B., and Mohammad-Djafari, A. 2005. Microwave imaging

of inhomogeneous objects made of a finite number of dielectric and con-

ductive materials from experimental data.
Inverse Problems, 21
, 95-115.

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