Image Processing Reference
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(a)
(b)
0
0
0.03
0.915
50
50
0.025
0.91
100
100
0.02
0.905
150
150
0.015
0.9
200
0.01
200
0.895
250
0.005
250
0.89
300
0
300
0
50
100
150
200
250
300
50 00
150 00
250 00
(c)
(d)
×10
-0
0
0
3.4
30.7
3.2
3
2.8
2.6
50
50
30.6
100
100
30.5
150
150
30.4
2.4
2.2
2
1.8
200
200
30.3
250
250
30.2
300
0
300
0
50
100
150
200
250
300
50 00
150 00
250 00
Figure 11.3
Comparison of reconstructed images from various method outputs for a target set consisting of a
circle with radius of
λ
, a square with sides of 2
λ
, and a triangle with base of 2
λ
and height of 3
λ
. All targets have
a permittivity of 1.9. 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 that are 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.
targets, but its attempt at defining the boundaries is fairly poor. The scale of
the magnitude for (d) is also very close in range for the index of refraction for
the targets which has an index value of 1.378.
While these demonstrations are encouraging and show great improvement
and promise, there are still two apparent immediate opportunities for future
research. The first is fairly straightforward in that the issue of the scale of
the new cepstrum method generated image is still not fully resolved. Great
improvements have been incorporated and we have a better understand-
ing than we have had in the past, but it is still not fully understood. Also,
there appears to be some other nonlinear dependence on either the number of
sources, the permittivity of the target or both. There may be other opportuni-
ties to remove or reduce the effects of the 〈Ψ〉 term in the cepstrum domain
much like the ones utilized previously in this topic.
11.2 An oveRAll AppRoACh to the degReeS oF
FReedoM In IMAgIng
It was noted earlier in this topic that, as experiments were being performed
on the minimum required number of receivers in relation to the degrees of
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