Spectral data arise in many scientific fields including biology, environmental monitoring, and astronomy. Physical laws and simplifying statistical assumptions motivate the idea that a mixed spectrum is approximately a linear combination of several constituent spectra. In the problems Dr. Bryan and his team consider the constituent spectra are derived from chemical components with known labels, while the non-negative weights of the linear combination represent the abundance of these chemicals in the mixture.

In this context, they propose strategies for using a dictionary of labeled spectra to estimate the abundance weights. The estimates they propose leverage statistical characteristics of spectral data in order to achieve lower variance than standard alternatives.

His team illustrates the use of these estimates on fluorescence spectroscopy measurements for water quality monitoring. Finally, he discusses the limitations of our approach as well as outstanding statistical questions, particularly as they relate to applications in astronomy such as quasar absorption line spectroscopy.