Image Processing Reference
In-Depth Information
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Figure 6.1 (a) Fourier representation from nine Ewald circles obtained from nine separate source directions
around a target. (b) Isometric view of Fourier domain image in (a).* (c) One Ewald circle indicated by an arrow in (a)
showing direction of incident wave, and resultant location of nonzero receiver data showing comparison to trans-
mission problem as the target or “transmission medium” is located in the center of the Ewald circle.
where the target volume is replaced with the target area A v . While the criteria
mentioned before * in the Fourier approach do have merit, it is really more
of a measure of the “weakness” of the scatterer and also of the validity of
the assumption that the incident field is linear inside the target. The recent
challenge is that this new criterion defined above could be a better gauge of
the performance or ability of an algorithm to reconstruct or “transmit” the
original target. In this application, it is suggested that the degrees of freedom
translate to the minimum number of independent target illumination direc-
tions or sources, or the minimum number of receivers or some combination
thereof necessary to fully “transmit” and “receive” all the information related
to the target. A series of experiments will be presented later to illustrate this
in the following sections. In particular, each aspect of this criterion will be
examined separately. More specifically, the degrees of freedom criteria will be
applied to the number of sources first, then, with some modifications, this cri-
terion will be applied to the number of receivers. Later in this topic, the idea
of an overall degrees of freedom requirement will be examined in more detail.
An attempt will be made to demonstrate that the degrees of freedom require-
ments for the number of sources and receivers spaced uniformly are impor-
tant. It is possible that these criteria can be combined to form a somewhat
* Note that if the target is a single point, then Figure 6.1b would be the point spread function.
 
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