Trend Filtering -- II. Denoising Astronomical Signals with Varying Degrees of Smoothness

Abstract

Trend filtering---first introduced into the astronomical literature in Paper I of this series---is a state-of-the-art statistical tool for denoising one-dimensional signals that possess varying degrees of smoothness. In this work, we demonstrate the broad utility of trend filtering to observational astronomy by discussing how it can contribute to a variety of spectroscopic and time-domain studies. The observations we discuss are (1) the Lyman-$\alpha$ forest of quasar spectra; (2) more general spectroscopy of quasars, galaxies, and stars; (3) stellar light curves with planetary transits; (4) eclipsing binary light curves; and (5) supernova light curves. We study the Lyman-$\alpha$ forest in the greatest detail---using trend filtering to map the large-scale structure of the intergalactic medium along quasar-observer lines of sight. The remaining studies share broad themes of: (1) estimating observable parameters of light curves and spectra; and (2) constructing observational spectral/light-curve templates. We also briefly discuss the utility of trend filtering as a tool for one-dimensional data reduction and compression.

Part 2 of 2, Link to Part 1: arXiv:1908.07151; 15 pages, 7 figures

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Cited by in corpus (3)

• Trend Filtering -- I. A Modern Statistical Tool for Time-Domain Astronomy and Astronomical Spectroscopy
• Deep Forest: Neural Network reconstruction of the Lyman-alpha forest
• An Optimized Ly$\alpha$ Forest Inversion Tool Based on a Quantitative Comparison of Existing Reconstruction Methods