Re: [APML] median vs. average vs. sigma

[Roland Roberts <roland@astrofoto.org>]

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>>>>> "Tony" == Tony Hallas <tonyhallas@foothill.net> writes:

    Tony> Median combining has a dirty little secret about it ... if
    Tony> all your frames are not EXACTLY similar, median combining
    Tony> will actually reject some of the frames

Unless I've badly misunderstood something, medium combining rejects
all but one of the values on a pixel-by-pixel basic.  With a even
number of frames, it will average a pair of values. 

There is a more sophisticated way of calculating a median for discrete
data but it is of limited utility for astronomy (see
http://www.ualberta.ca/CNS/TSQS/median.html).

The main reason for doing a median combine is to eliminate outliers.
Got a dust speck on one of your five images?  It will (probably)
disappear in a median combine but still be visible in a mean.

Statistically, for your normal (as in bell-curve) distributed data,
calculating the mean and the median will give the same result.  Of
course, for most of us, we don't have enough images to insure we have
a statistically valid sample.

You might also find this interesting,

    http://www.rc-astro.com/resources/sigma_reject.html

which points out that while you do have an increase in S/N with a
median combine, it is not as bad as a naive estimate might make you
think.  If, after all, you have frames and are effectively only using
the info from one (but on a pixel-by-pixel basis, so it is garnered
from all 9), you might think your S/N is only as good as one image.
It's better, but (in this example), it's about equivalent to using
only 6 of the 9.

regards,

roland
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		       PGP Key ID: 66 BC 3B CD
Roland B. Roberts, PhD                             RL Enterprises
roland@rlenter.com                            6818 Madeline Court
roland@astrofoto.org                           Brooklyn, NY 11220

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