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ABSTRACT: A new reconstruction algorithm for diffraction tomography is
presented. The algorithm is based on the minimization of a functional
which is defined as the norm of the discrepancy between the measured
scattering amplitude and the calculated one for an estimated object
function. By using the conjugate gradient method to minimize the
functional, one can derive an iterative formula for getting the object
function. Numerical results for some two-dimensional scatterers show
that the algorithm is very effective in reconstructing refractive index
distributions to which the first-order Born approximation can not be
applied. In addition, the number of iterations is reduced by using a
priori information about the outer boundary of the objects. Furthermore,
the method is not so sensitive to the presence of noise in the scattered
field data
IEEE Transactions on Antennas and Propagation 09/1995; · 2.15 Impact Factor
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ABSTRACT: Several inversion algorithms for diffraction tomography have
previously been provided in a wide range of situations where the
first-order Born or Rytov approximation fails. These algorithms are
based on the assumption of full field data so that it is assumed that
both intensity and phase of the scattered field are measurable. However,
it becomes difficult to measure the phase of the scattered field
directly, if the frequency of the incident wave is beyond several tens
of GHz. Therefore, some intensity-only reconstruction algorithms for the
objects within the first-order Born or Rytov approximation were
proposed. The present authors give an intensity-only reconstruction
algorithm for the scatterers beyond the first-order Born approximation.
This algorithm is based on the optimization method minimizing a
functional which is the norm of the discrepancy between the measured
intensity of the total field in the far-zone and the calculated one for
an estimated object function. An outer boundary of the scatterer is used
as a priori knowledge at each step of iteration. The proposed algorithm
is an extension of Takenaka et al. (1993)
Antennas and Propagation Society International Symposium, 1994. AP-S. Digest; 07/1994
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ABSTRACT: Presents an iterative inversion algorithm of reconstructing two-dimensional buried dielectric objects in a cross-well geometry. We define a cost functional as the norm of the discrepancy between the measured scattered field and the calculated one for an estimated object function. Note that the object function is related to the refractive index of the object. Then the inverse scattering problem reduces to an optimization problem where the object function is determined by minimizing the functional. Applying the conjugate gradient method to the optimization problem, one can derive an iterative formula for deriving the object function. Numerical results are presented for a lossy and homogeneous dielectric circular cylinder. The results demonstrate that the proposed algorithm yields high-quality reconstructions even for cases where the Born or the Rytov approximation breaks down
Antennas and Propagation Society International Symposium, 1994. AP-S. Digest; 07/1994
