Image Processing Reference
In-Depth Information
Advanced Cepstral Filtering
10.1 Independent pRoCeSSIng oF SouRCe dAtA
It has been shown in a previous work that improvements can be made to a
reconstructed image produced by using the Born approximation method by
performing filtering in the cepstrum domain (Shahid, 2009). Previously in
applying this method, the filtering was applied to the V 〈Ψ〉 image data from
the combined sources. In retrospect, while the expectation was that the field
term might appear noise-like, a more rigorous approach is described here. The
basis of the derivation in Chapter 4, in particular Equations 4.28 through 4.31,
is that it is for a single incident wave or direction. Since this is the case, it
seems logical that the processing of the data should be carried out on a source-
by-source basis and then recombined later in the process. When the indepen-
dent source data is combined at the beginning, this gives the opportunity for
the information relating to the unwanted Ψ terms to be combined and possibly
modulated in such a way that parts of its spectrum may be even more difficult
to locate and/or remove.
This being the case, the cepstrum filtering method in Shahid (2009) has
been re-implemented on a source-by-source basis in lieu of a combined source
method. To accomplish this, the Ewald circle of data for each independent
source was derived separately and the Born image for each source was com-
puted as illustrated in Table 10.1 for two different target sets, a circle and two
triangles. The data for each source was then transformed into the cepstrum
domain and filtered accordingly as before in Shahid (2009), again as illustrated
in Table 10.2 for these two different targets sets. The question then arises at to
what is the optimum step in the reconstruction process to recombine the inde-
pendent data into a cumulative data set from which the entire image could be
recovered. There are two opportunities to do this. The first is in the cepstrum
domain directly after filtering The second is to transform each of the inde-
pendent filtered source data back into the image domain and recombine there.
Both of these scenarios have been implemented and will be examined.
This total process was performed on four unique target sets to provide a
broad comparison of the general performance of these methods. Four target
sets with various permittivities were modeled and filtered as described above
(Table 10.3). As seen in Table 10.3, it is obvious that all of the cepstrum fil-
tered images show improvement over the image obtained using just the Born
method, both in regard to image boundaries as well as noise reduction. In
the analysis of these methods, it has been observed that as the permittivity
of a target is increased, the apparent size of the resulting target reconstruc-
tion using the Born approximation method is artificially inflated in relation
to the actual target size. This can be seen in the images shown in Table 10.3.
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