Robust joint estimation of galaxy redshift and spectral templates using online dictionary learning
Sean Bryan, Ayan Barekzai, Delondrae Carter, Philip D. Mauskopf, Julian Mena, D. Rivera, Abel S. Uriarte, Pao-Yu Wang · Astronomy and Astrophysics · 2026
Context . 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. Aims . We address these limitations by developing a new algorithm that jointly estimates both the underlying spectral features in common across the entire dataset, as well as the redshift of each galaxy. Methods . To do this, we significantly extend an existing online dictionary learning algorithm, and apply this approach to redshift estimation for the first time. Results . Our new 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 normalized median absolute deviation (NMAD) 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 (S/N), delivering sub-percent NMAD and catastrophic error above median S/N of 20. We released our algorithm publicly and it is available on GitHub.