| Summary: | 碩士 === 國立海洋大學 === 電機工程學系 === 88 === Iterative methods are suitable for solving large-sized problems
in the electromagnetic wave scattering. The conjugate gradient method
combined with the fast Fourier transform (CGFFT) is an efficient solver
in the forward scattering problems.
In microwave imaging, material permittivity is the parameter to retrieve.
Traditionally, the standard method used is to minimize the cost function
with Tikhonov regularization. This method can retrieve smooth object
functions successfully, but there is serious Gibbs phenomenon appearing
near the neighborhood of discontinuous boundaries in the reconstructed
images. The total variation (TV) regulated method for retrieving the
discontinuous object functionsas well as denoising has been proposed
recently and been proven very successful for both retrieving the profiles
at sharp boundaries and denoising.
In this thesis, we use the conjugate gradient method (CGM) and the
variable metric method (VMM) to minimize the cost function regulated
by the total variation, respectively. Both methods require the first
derivative calculation. We analyze the factors which influence the
results of reconstructions, propose some empirical values or formulas
to the relative parameters, and point out the differences and similarities
between CGM and VMM. We also use the multiple frequency scheme
to reconstruct the image of a large-sized object which is a biological model
of human arm. We applied the TV enhanced method at the highest frequency
reconstruction and have obtained a very good result.
Parallel processing has become a tendency to reduce the heavy load
of computational-intensive problems. The inverse scattering problem is
one of this kind. So, it is feasible to apply the parallel processing techniques
in the minimization process for profiles reconstruction. We have parallelized
the inverse scattering algorithms which employ different numerical methods,
analyzed the relative efficiencies and the factors which influence them.
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