Image Processing Reference

In-Depth Information

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Figure 9.16
FoamDielInt at 6 GHz: (a) Born reconstruction with DFT, (b) cepstral reconstruction using DFT,

(c) Born reconstruction using PDFT - a square prior, (d) cepstral reconstruction using PDFT - square prior, (e) Born

reconstruction using PDFT - circular prior, and (f) cepstral reconstruction using PDFT - square prior.

cepstral filtering with the DFT, since the background permittivity level has

to be the lowest level for this object. Figures 9.16d and 9.16f show that the

PDFT has addressed this problem of an incorrect background permittivity.

The effect of two different prior functions used with the PDFT is also shown:

one a square and the other a circle. The improvement using these is signifi-

cant, and the choice of prior is not that critical, as expected when it is large

compared with
V
. Considering the fact that FoamDielInt is a strong scattering

object, even first Born reconstructions have shown some improvement with

the use of PDFT, as is evident from Figures 9.16a and 9.16c.

Since each illumination frequency generates a different
V
(
r
)〈Ψ〉 with
V

being the same and 〈Ψ〉 different for each wavelength, it follows that each

illumination frequency provides us with different information and useful

redundancy. In other words, changing the frequency of the incident field will

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