Image Processing Reference

In-Depth Information

table 11.1
Ewald Circle Sets with Accompanying Born

Reconstructed Images for a Series of Source/Receiver

Combinations All Totaling 216 Receivers (or Data Points) with

Random Spacing Applied to the Receiver Locations about Their

Original Equispaced Locations

Src
=
9; Rec
=
24

Src
=
12; Rec
=
18

Src
=
18; Rec
=
12

Src
=
36; Rec
=
6

Note:
Target used is a square with sides equal to 2
λ
and a permittivity of 1.5. Src,

source; Rec, receiver.

freedom, a randomness was injected into the receiver locations to address

aliasing. In this process, there came a point where it was difficult to distin-

guish the number of sources from the number of receivers that were actu-

ally present. It had begun to look more like as if it was a matter of the total

number of receiver points (and possibly their distribution) more than how

many sources there were, that is, perhaps the more important metric is the

total number of data points that are evenly distributed. This is illustrated in

Table 11.1. For each of the set of Ewald circles and image reconstructions, the

total number of receiver or data points is the same, which is 216. Because they

are randomly spaced (at least around their original locations), it is difficult to

distinguish between the Ewald circle sets since the resulting images appear

to be very similar in appearance. This would seem to suggest that possibly

the minimum requirement is not so much a function of the number of sources

and/or the number of receivers required, but more the total number of receiver

or data points equally but randomly spaced to fill the
k-
space area. If this is

the case, then it is possible that the minimum degrees of freedom may not be

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