Advanced Topics in Inverse Imaging - Introduction to Imaging from Scattered Fields - page 175

Eleven
Advanced Topics in Inverse Imaging
11.1 pRACtICAl StepS FoR IMAgIng StRong SCAtteReRS
Up to this point in this topic, a gradual and historical review has been pre-
sented on approaches and advances in imaging from scattered electromagnetic
fields In the midst of this review, some very recent and significant techniques
and observations have been presented that show great advancement in this
field in the recent years. To demonstrate these advancements and techniques,
a brief review and comparison will now be presented.
The first significant technique that was presented was that of the capability
of creating a virtual test setup in a finite element modeling software such as
COMSOL ® to model scattered field data from a representative family of known
targets. It was then shown how this data could be imported into MATLAB ® for
processing and investigating various algorithms and methods. It was demon-
strated that this task can be successfully completed and that the results from
using this structured approach can be used to produce results that are com-
parable to the results from experimental data when adopting the exact same
experimental conditions. This new method, now validated, proves to be indis-
pensible in producing data for many different scattering conditions that are
essential in addressing the other objectives. With the use of this method and
the data that it produces, existing methods and algorithms can continue to be
studied and evaluated in a way that would be virtually impossible in a labora-
tory setting. This algorithm should prove to be very useful in future research
dealing with other inverse problems, scattering, and imaging studies.
Using methods much like the one described above, data can now be gener-
ated that will allow the Born approximation and its corresponding images
to be examined with great detail. In particular, the concept of the number of
degrees of freedom associated with a scattering or imaging experiment that
had been suggested in previous research (Miller, 2007) was put to the test.
The concept of degrees of freedom for 2-D imaging from scattered field data in
terms of the number of sources and receivers was studied for numerous con-
ditions and targets. As demonstrated previously, this measure of information
transfer in a scattering experiment in relation to the use of the Born approx-
imation does seem to be valid. The degrees of freedom for each simulated
experiment can be calculated, and for each case this number can be regarded
as a threshold identifying the point at which the reconstructed images begin
to achieve a “steady state” in their appearance. As also seen previously, this
is not to say that the images at this point are “good” or that they model the
original target exactly, since this depends on the extent of the multiple scat-
tering, but that these reconstructions did not appear to show any significant
improvement when using additional sources or receivers beyond this point.
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