Estimating Background Spectra

All measurements consist of a mixture of the signal of interest and additional signals called the background. Here we focus on the problem of measuring infrared spectra emitted by interstellar clouds. The signals of interest are infrared emissions from polycyclic aromatic hydrocarbons (PAHs), which are a class of complex organic molecules. The PAH emissions are characterized by emission bands near 3.3, 6.2, 7.7, 8.6, 11.2, and 15-20 microns. The background consists of a host of associated spectral signals which, in the simplest case, can include emissions from multiple Planck blackbodies as well as broadband and narrowband emissions. To analyze the PAH spectra we must accurately assess this background. To do this, we have developed a Bayesian algorithm based on nested sampling (Skilling 2005, Sivia & Skilling 2006). The spectral model consists of a mixture of Planck functions and Gaussians. We demonstrate this algorithm on both synthetic data and infrared spectra recorded from interstellar clouds. The result shows that the algorithm can accurately identify and remove simple backgrounds. In future work, we plan to incorporate mixtures of PAH spectra and more complex models for the background so that the algorithm will simultaneously estimate both the signals of interest and the background.