Imagine, you get a letter from Gauss. Of course the letter will not be addressed to you personally. In our case, the letter was addressed to Bessel, dated 1839 Febr 28, and we received it with kind permission of the Niedersächsische Staats- und Universitätsbibliothek Göttingen to use it as part of the cover art for our preprint series.
What we actually got was a photocopy, and the data we worked on was a scanned grey level TIFF image of this photocopy. The challenge was to create a reconstruction from these data which could serve as a printable master. Of course the letter was aged. The most obvious effect was that the ink had diffused into the paper. The contours of the writing had blurred out, and at some parts the continuity of the contours was broken.
There was a general background error, resulting form paper and ink diffusion. The amount of degradation can be best seen from a false colour image of one paragraph of the letter.
Imagine you got this letter. You have to clean it up.
If you think in terms of image analyis, you have to reconstruct an image.
If you think in statistical terms, you have to estimate the original writing from the observed data stored in the TIFF file representig the grey level matirx of pixels.
Good luck. You get information about the data set from <http://statlab.uni-heidelberg.de/data/gauss/www.html>. If you want to see one solution for this data set, go to the bottom line of the "Beiträge zur Statistik".
Here is a fist observation which may help in the analysis and reconstruction: Gauss had a very neat uniform handwriting, and the error, or degradation, has various distinct non-uniform structures. The neat handwriting of Gauss makes the reconstruction task easier. You can analyse his writing style from a general analysis, and then use the a priori information for the reconstruction steps. As far as the degradation are concerned, it may be helpful to think of several degradation processes, or error contributions.
Our result is at the bottom line of the " Beiträge zur Statistik".