Image Processing Reference
In-Depth Information
is done in an attempt to reduce or eliminate the 〈Ψ〉/ R ′ term in the cepstrum
domain representation of the signal. The results of applying this additional
“filtering” step proved to be very promising in that it appears to improve the
scale of the magnitude of the reconstructed image resulting from the “com-
bined in cepstrum space” method. In fact, as shown in the previous results,
the peak of the scale is very near the “correct” value for the permittivity (or
better yet, to the index of refraction) of the original target.
If we now take all of the improvements mentioned above, that is, processing
sources independently, optimized filtering, and subtracting the incident field
in the cepstrum domain, we can apply these new and improved methods to
a more complex target set and compare its results to those obtained by using
previous methods to observe the progression of improvements. This was done
for a target set consisting of a circle with radius of λ, a square with sides of
2λ, and a triangle with a base of 2λ and a height of 3λ. This concluding test
was run three times with the targets having a permittivity of 1.1, 1.5, and 1.9
respectively to observe how the methods performed in relation to each other.
The results of this set of demonstration experiments are shown in Figures
11.1 through 11.3 below. The results shown in Figure 11.1 are extremely
(a)
(b)
×10 -0
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0.905
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0.9
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0.895
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0.89
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0.885
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0.875
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0.87
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(c)
(d)
×10 -0
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1.8
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1.6
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Figure 11.1 Comparison of reconstructed images from various method outputs for a target set consisting
of a circle of radius λ , a square with sides 2 λ , and a triangle with base 2 λ and height 3 λ . All targets have a
permittivity of 1.1. The outputs shown above are from (a) Born approximation, (b) cepstrum of image in (a) using
algorithm developed in Shahid (2009), (c) cepstrum filtering of individual sources recombined in image space, and
(d) cepstrum filtering of individual sources that are recombined in image space and have a cepstrum version Ψ in
subtracted in cepstrum space.
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