| fitting many linear eqs simultaneously with outliers [message #77982] |
Wed, 12 October 2011 22:01 |
Jeremy Bailin
Messages: 618
Registered: April 2008
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Senior Member |
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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.
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