separating noise from signal

Or Graur (JHU), Yuqian Liu (NYU), Maryam Modjaz (NYU), and Gabe Perez-Giz (NYU) came by today to pick my brain and Fadely's brain about interpreting spectral data. Their problem is that they want to analyze supernova spectral data, but for which they don't know the SN spectral type, don't know the velocity broadening of the lines, don't know the true spectral resolution, don't know the variance of the observational noise, and expect the noise variance to depend on wavelength. We discussed proper probabilistic approaches, and also simple filtering techniques, to separate the signal from the noise. Obviously strong priors on supernova spectra help enormously, but the SN people want to stay as assumption-free as possible. In the end, a pragmatic filtering approach won out; we discussed ways to make the filtering sensible and not mix (too badly) the signal output with the noise output.