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Re: fitting many linear eqs simultaneously with outliers [message #77923]

Mon, 17 October 2011 23:56

Jeremy Bailin
Messages: 618
Registered: April 2008

Senior Member

On 10/13/11 1:01 AM, Jeremy Bailin wrote:
> So I have a large number of very simple linear equations, which all look
> like:
>
> a_i + b_i x_ij = a_k + b_k x_kj
>
> for i,k=1..N (all unique combinations of i and k), j=1..M. The data
> values x_ij and x_kj are measurements of the brightness of object j in
> images i and k respectively, where the images have an unknown zero point
> and scalings that I am trying to determine.
>
> (aside to astronomers: this may sound suspiciously like re-implementing
> mscimatch)
>
> Not all objects appear in all images, so there are different numbers of
> equations relating each pair of images. In principle, any number of
> linear solvers should work... BUT: it needs to be extremely robust to
> outliers. I know for a fact that there are many many many outliers, and
> there are some pairs of images where it looks like pure scatter. So I
> need some sort of solver that will do sigma clipping. Essentially, I
> want a sigma-clipping linear least squares solver that can solve more
> than one line at once.
>
> Does anyone know of such a beast already existing? Or something that's
> vaguely similar enough that I can use it as a basis?
>
> -Jeremy.

In case anyone cares, my solution was to get the user's brain (in this
case, my undergrad) to do the hard work. I plotted up all the points for
each possible pair of image combinations, got them to draw the best fit
line on there, finessed it a little with a linear fit to only those
points very close to the drawn line, and then solved for the best global
solution for all images using singular value decomposition. Certainly
not the most automated solution, but the results are beautiful. And my
first ever IDL widget program...

-Jeremy.

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[Message index]

		Re: fitting many linear eqs simultaneously with outliers By: Jeremy Bailin on Mon, 17 October 2011 23:56
		Re: fitting many linear eqs simultaneously with outliers By: Craig Markwardt on Fri, 14 October 2011 18:46
		Re: fitting many linear eqs simultaneously with outliers By: Bringfried Stecklum on Fri, 14 October 2011 02:32
		Re: fitting many linear eqs simultaneously with outliers By: Matt Francis on Thu, 13 October 2011 22:37

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