We're going to assume for starters that the black spots are grey (constant attenuation as a function of wavelength). We can't assume that the attenuation is identical for all fibers.

rhl has suggested that solving for the profiles might be done by matrix inversion. But it seems to me that the model is non-linear in the parameters, as we're fitting:

flux(image, x, y) = A_{image, fiber} . B_{fiber, x, y}

where A is the normalisation for a particular fiber on a particular image, and B is the fiber profile.

If we were to fit log(flux) the equation would be linear, but then it's not linear in flux and Bad Things would surely happen.

One thing to think about is measuring a guess for A directly from the data (e.g., starting with a narrow boxcar extraction) and solving for B. Then we could iterate a few times in an attempt to atone for errors in our starting assumption.

I've come fairly close to getting this working well, but I've hit a roadblock when fitting profiles in the integration test: the matrix solution is taking a crazy long time with the default solver, and other solvers either fail or segfault. But the matrices are fine when I run them through the Eigen sparse matrix benchmark program. I'm hoping that a more recent version of Eigen will deal with whatever is causing this, so will put this back on the stack until after PIPE2D-598, and deal with more pressing issues.

Hmm. Are you sure that there's not a memory problems somewhere?

Thanks for the idea. I found a memory problem in my code, but fixing that didn't help the segfaults and such in the matrix solver.

You shouldn't be able to get segfaults from a bad matrix, especially if it solves stand-alone.

price Where do we stand on merging this ?

Merged a couple of weeks ago.