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Abstract:
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The problem of denoising a one-dimensional signal possessing varying degrees of smoothness is ubiquitous in time-domain astronomy and astronomical spectroscopy. In this work, we introduce trend filtering into the astronomical literature. Trend filtering is a modern nonparametric statistical tool that yields significant improvements in the broad problem space of denoising spatially heterogeneous signals. When the underlying signal is spatially heterogeneous, trend filtering is superior to any statistical estimator that is a linear combination of the observed data—including kernels, LOESS, smoothing splines, and Gaussian process regression. Furthermore, the trend filtering estimate can be computed with practical and scalable efficiency via a specialized convex optimization algorithm. In order to illustrate the broad utility of trend filtering, we discuss its relevance to a diverse set 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 transiting exoplanet(s); (4) eclipsing binary light curves; and (5) supernova light curves.
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