The region of the image which is searched for the peak can be limited to those areas (known as the `CLEAN' windows or boxes) within which emission is presumed to be present. These boxes restrict the number of degrees of freedom available when fitting the data. Schwarz's work (and common sense) tells us that the number of such degrees of freedom should be minimized but that the `CLEAN' window should include all real emission. For a simple source in an otherwise uncluttered field of view, one `CLEAN' window will do, but multiple boxes may be needed when `CLEAN'ing more complicated sources, or a field containing many sources. In the latter case, the presence of weak sources may be revealed only after the sidelobes of the stronger sources have been removed, so more boxes may be needed as the `CLEAN' progresses. (Note that such a posteriori definition of `CLEAN' boxes complicates any noise analysis.)
It is hard to gauge the practical implications of Schwarz's
observation that the number of degrees of freedom should not exceed
the number of independent constraints. In the presence of noise,
u,v samples can be judged independent if the differences in
visibility due to the size of structure expected are much greater than
the noise. Counting visibility points in such a way, the aggregate
area of the `CLEAN' boxes in pixels should be less than twice the
number of independent visibility samples. If the FFT is used,
then the number of independent visibility samples cannot be greater
than 
, so it is advisable to use `CLEAN' boxes.
Given the uncertainty in determining the number of independent data
points, and hence the number of constraints, caution dictates that
boxes should always be placed tightly around the region to be `CLEAN'ed.
1996 November 4
10:52:31 EST