Roweis and I realized today that we should enforce much more than smoothness on the matrix that relates flux (in the observed object) to pixel values (in the CCD); we know that the matrix can be thought of as a narrow spectral trace convolved with an aperture-convolved, pixel-convolved point-spread function. So we should just model these two things (trace and PSF), and enforce smoothness there. That represents much stronger prior information for our inference, but it is sensible, in the sense that if we inferred a matrix that does not look like a trace convolved with a (slowly varying) PSF, we wouldn't believe it. We also worked out a bit about how to proceed.
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