Image Processing Reference
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.
Abubakar, A., vand den Berg, P. M., and Habashy, M. 2005. Application of the
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.
Search WWH ::