  We present a novel approach to analyzing astronomical spectral survey data
using our non-linear extension of an online dictionary learning algorithm.
Current and upcoming surveys such as SPHEREx will use spectral data to build a
3D map of the universe by estimating the redshifts of millions of galaxies.
Existing algorithms rely on hand-curated external templates and have limited
performance due to model mismatch error. Our algorithm addresses this
limitation by jointly estimating both the underlying spectral features in
common across the entire dataset, as well as the redshift of each galaxy. Our
online approach scales well to large datasets since we only process a single
spectrum in memory at a time. Our algorithm performs better than a
state-of-the-art existing algorithm when analyzing a mock SPHEREx dataset,
achieving a NMAD standard deviation of 0.18% and a catastrophic error rate of
0.40% when analyzing noiseless data. Our algorithm also performs well over a
wide range of signal to noise ratios (SNR), delivering sub-percent NMAD and
catastrophic error above median SNR of 20. We released our algorithm publicly
at github.com/HyperspectralDictionaryLearning/BryanEtAl2023 .
