Image Processing Reference

In-Depth Information

unified degrees of freedom criterion. Experiments are carried out to test this,

and speculation is made as to the exact form of this alternate requirement.

6.2 RequIReMentS FoR degReeS oF FReedoM FoR SouRCeS

For the purpose of demonstrating the role of degrees of freedom and its useful-

ness in predicting performance when imaging from scattered fields, a series or

“families” of reconstructed images will now be presented. These reconstruc-

tions are presented in a systematic way for a group of selected targets, all illu-

minated by an increasing number of incident waves, all with a frequency of

5 GHz. The targets of choice for this demonstration are defined and described

in Table 6.1.

For each of these target parameters, the degrees of freedom and the weakly

scattering metric (
kVa
), discussed in Section 6.1, are calculated and shown

for reference. Also, to aid in the analysis of these images, the borders of each

image are shaded in either “red” or “green,” with “red” indicating that for the

given parameters and number of sources, the minimum degrees of freedom

are not satisfied, and the “green” indicating that for the given parameters and

number of sources, the minimum degrees of freedom are satisfied With this

color code the reader should be able to distinguish, as the number of sources

is increased (moving “down” the table), when the minimum criteria are met.

It should be noted that there are obviously other factors that are affecting

the reconstruction in these images, namely obvious resonances that occur for

different parameters that definitely affect some of the images as compared to

others. These phenomena will be examined in more detail in the following

sections. It should also be kept in mind that the measure of and meeting of the

number of degrees of freedom do not necessarily indicate that the image will

look exactly like the target because the challenges and issues involved with

the inverse scattering problem remains; it simply means that for the given

parameters, adequate sources have been used to “communicate” or transfer as

much information about the target as is possible under the given experimental

arrangement. So, with this in mind, one would expect that after the minimum

degrees of freedom have been met, and for all images with higher degrees of

freedom, the image of the “target” should not change significantly from one

image to the next. This is not to say that the entire image will not change as

there could be significant differences in the “noise” artifacts in the free space

table 6.1
Definition of Various Target Types and Scenarios

Used to Test the Degrees of Freedom Requirement along with

Corresponding Table Number of Results

table number

shapes

Dimensions

Permittivity Range

5.2

1 Circle

Radius
=
1
λ

2-10

5.3

1 Circle

Radius
=
1
λ

11-19

5.4

1 Circle

Radius
=
2
λ

2-10

5.5

2 Circles

1.1-1.9

Radius
=
1
λ

5.6

2 Circles

Radius
=
1
λ

2-10

5.7

1 Square

Sides
=
1
λ

1.1-1.9

5.8

2 Squares

1.1-1.9

Sides
=
1
λ

5.9

2 Triangles

Base/height
=
2
λ
/3
λ

1.1-1.9

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