  Survey-based measurements of the spectral energy distributions (SEDs) of
galaxies have flux density estimates on badly misaligned grids in rest-frame
wavelength. The shift to rest frame wavelength also causes estimated SEDs to
have differing support. For many galaxies, there are sizeable wavelength
regions with missing data. Finally, dim galaxies dominate typical samples and
have noisy SED measurements, many near the limiting signal-to-noise level of
the survey. These limitations of SED measurements shifted to the rest frame
complicate downstream analysis tasks, particularly tasks requiring computation
of functionals (e.g., weighted integrals) of the SEDs, such as synthetic
photometry, quantifying SED similarity, and using SED measurements for
photometric redshift estimation. We describe a hierarchical Bayesian framework,
drawing on tools from functional data analysis, that models SEDs as a random
superposition of smooth continuum basis functions (B-splines) and line
features, comprising a finite-rank, nonstationary Gaussian process, measured
with additive Gaussian noise. We apply this *Splines 'n Lines* (SnL) model to a
collection of 678,239 galaxy SED measurements comprising the Main Galaxy Sample
from the Sloan Digital Sky Survey, Data Release 17, demonstrating capability to
provide continuous estimated SEDs that reliably denoise, interpolate, and
extrapolate, with quantified uncertainty, including the ability to predict line
features where there is missing data by leveraging correlations between line
features and the entire continuum.
