Well, what I'd "pull first out of my pocket" concerns Fourier Transform (FT)
methods. Further below, I will illustrate the particular power of using FT transform pairs for removing periodic structures with an instructive 2D example that I came across in the net. http://www.robots.ox.ac.uk/~az/lectures/ia/lect2.pdf
What's the trick? FT maps periodic
signals into needle fine peak patterns, a dominating primary peak along with a number of secondary ones. Of course the primary peak position in Fourier space corresponds to the frequency of the periodiicity in real space.This fact guarantees that the modification of unwanted periodic stripe patterns (Gaia!
) can be done with minimal amount of distortion of other non-periodic data!
Now look at the mentioned 2D example ("Forensic application") that should essentially be self-explaining:[click on image by all means for an adequate size]
FT_example.jpg [ 87.97 KiB | Viewed 319 times ]
Start with the top-left image that features (probably;-)) a woven table cloth with a doubly periodic weaving pattern along with a stain due to a finger print. After 2 dimensional FT, one obtains the red image on top right ( in Fourier space). Note the set of dominating very narrow peaks that now comprise ALL data associated with the original periodic background. The rest of the data is smeared out and thus entirely different in structure from the isolated peaks. What remains is just to remove the narrow peaks in Fourier space (see the red image on bottom right) and to transform the slightly modified data back into real space. The result looks pretty good (image on bottom left). The periodic background is entirely gone.
But for the Gaia DR1 stripe issue there is much more one will have to investigate, since there is always the aspect of positional star precision that will continuously compete with any such modification. Note also that we have a 3D problem with Gaia, not 2D as in the example.
So far I consider these FT activities more like a game one could play with. But I don't take them seriously for various reasons....
Anyway, let's see what Andrew's ideas look like...