[Aavso-photometry] average vs. median

[Michael Newberry]

Hi Tomas.

I had written this and Arne's post came in. He says pretty much what I had 
to say. I would add the importance of saving the combined image to real type 
pixels rather than integer type pixels. Also I'll give a link to an 
experiment I did years ago comparing the various options.

[... see Arne's post]

Another thing to consider about combining images is whether the images are 
stored as real numbers or integral numbers. As the number of combined frames 
tends to infinity, the mean value is gets refined more and more so that the 
error of the mean tends toward zero. Saving the result as integral values 
requires the nearest whole number to be chosen---which, after some point, 
wipes away further gains in noise reduction. Using the median also has the 
undesirable effect that the median value itself can use only the values 
already in the set. When combining images that have integral values, the 
median value gets stuck between the two nearest integral values (or half 
integral if you are using the half value for an even numbered set).

There's an old-old-old (but still valid) example showing real results for 
combined images on our website at  http://www.mirametrics.com. From the left 
menu bar, select "Virtual Library", then item 5, "Combining Images with 
Integer and Real Pixel Values." This Tech Note shows how mean-combining 
acheives a smaller noise level and how saving to a real type image decreses 
the noise even further.

Michael Newberry


----- Original Message ----- 
From: "Tomas L. Gomez" <tomas.l.gomez at gmail.com>
To: <Aavso-photometry at mira.aavso.org>
Sent: Friday, January 20, 2006 3:39 AM
Subject: [Aavso-photometry] average vs. median


> If I have N measurements, each one with error sigma,
> and I take the average, then the error will be reduced
> to sigma/sqrt(N).
>
> If, instead of taking the average, I take the median,
> how is the error reduced?.
>
> Knowing this could be very useful to decide whether
> to use the median of the average when stacking images,
> for instance.
>
> Thank you in advance for any help anyone can give.
>
> -Tomas L. Gomez (GOT)
>
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