Image Processing Reference

In-Depth Information

Nine

Applications to Real

Measured Data

9.1 IpSwICh dAtA ReSultS

In this section, various methods are applied to real data provided by various

groups. The US Air Force Research Laboratory (AFRL) initiated the idea that

it would be beneficial for the inverse scattering community to test their algo-

rithms on measured data from unknown targets. They conducted a number of

scattering experiments and provided scattered field data, known as Ipswich

data, in the mid-1990s (McGahan and Kleinman, 1999) and which has still

kept the community busy since then. More recent data sets have been the

focus of special issues of journals such as inverse problems using data pro-

vided by the Institut Fresnel (McGahan and Kleinman, 1999). In addition, the

proposed methods in this topic are applied on the analytic data to study the

effect of sampling on the inverse scattering problem.

The AFRL collected Ipswich data in an anechoic chamber, using the

swept-bistatic system described in Maponi et al. (1997). Figure 9.1 taken from

McGahan and Kleinman (1999) shows the layout of the measurement system,

and defines the angles used to describe the data.

9.1.1 IpS008

First we perform the minimum phase procedure on Ipswich data sets IPS008

and IPS0010, the strong scatterers. The IPS008 test subject consists of two

cylinders; the outer cylinder is filled with sand and the inner cylinder is filled

with salt. The cylinder is placed far enough from the source to ensure that the

illuminating wave is well approximated by a plane wave.

The measured and limited data consisted of 36 illumination directions,

at equal angular separations of 10° and 180 complex scattered field measure-

ments for each view angle using a frequency of 10 GHz. These data were

located on arcs in
k
-space and moved into one quadrant to impose causality.

The IPS008 object represents a strongly scattering penetrable object and has

proved to be one of the most difficult to recover from its scattered field data

(McGahan and Kleinman, 1999). The geometry of IPS008 is shown in Figure

9.2a; the best image one could expect from the available scattered field mea-

surements, assuming only an inverse Fourier transform is necessary over the

loci of data circles in
k
-space, is shown in Figure 9.2b.

Figure 9.2c shows a reconstruction from the nonlinear filtering method.

The reference point,
R
, introduced at the origin in
k
-space was increased until

the phase of
V
() (, )

Ψ
·
lies between +π and −π. A Gaussian low pass filter

was then applied until all wave-like features had been eliminated from the

r

〈

r r

〉

117

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