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Abstract:
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Electromagnetic tomography has been applied to problems in
nondestructive evolution, ground-penetrating radar, synthetic aperture
radar, target identification, electrical well logging, medical imaging
etc. The problem of electromagnetic tomography involves the
estimation of cross sectional distribution dielectric permittivity,
conductivity etc based on measurement of the scattered fields. The
inverse scattering problem of electromagnetic imaging is highly non
linear and ill posed, and is liable to get trapped in local minima. The
iterative solution techniques employed for computing the inverse
scattering problem of electromagnetic imaging are highly computation
intensive. Thus the solution to electromagnetic imaging problem is
beset with convergence and computational issues. The attempt of this
thesis is to develop methods suitable for improving the convergence
and reduce the total computations for tomographic imaging of two
dimensional dielectric cylinders illuminated by TM polarized waves,
where the scattering problem is defmed using scalar equations. A multi
resolution frequency hopping approach was proposed as opposed to
the conventional frequency hopping approach employed to image large
inhomogeneous scatterers. The strategy was tested on both synthetic
and experimental data and gave results that were better localized and
also accelerated the iterative procedure employed for the imaging. A
Degree of Symmetry formulation was introduced to locate the scatterer
in the investigation domain when the scatterer cross section was
circular. The investigation domain could thus be reduced which
reduced the degrees of freedom of the inverse scattering process. Thus
the entire measured scattered data was available for the optimization of
fewer numbers of pixels. This resulted in better and more robust reconstructions of the scatterer cross sectional profile. The Degree of
Symmetry formulation could also be applied to the practical problem
of limited angle tomography, as in the case of a buried pipeline, where
the ill posedness is much larger. The formulation was also tested
using experimental data generated from an experimental setup that was
designed. The experimental results confirmed the practical
applicability of the formulation. |