Optical Spectroscopy Sequential Wavelength Selection Using a Higher Leverage Approach

The problem of minimizing wavelength usage and, therefore, decreasing measurement time in spectroscopy experiments has been studied over the years, under many different scenarios. These solutions offer optimal or suboptimal
$N$
wavelengths for systems with
$N$
substances. In this letter, we propose a deterministic algorithm for wavelength selection for substance detection and classification of spectral data, generated by overdetermined systems, that is, when the number of wavelengths is greater than the number of substances. This type of problem is common when the increasing popular low signal-to-noise portable thermal sensors are used. A cardinality penalizing constrained multivariate regression is also proposed as the criterion for evaluating the mean-squared error. As a practical example, the spectrum of five different substances [i.e., 1) lignin, 2) cellulose, 3) petroleum jelly, 4) pentaerythritol tetranitrate, and 5) hexamine] were chosen as a proof of concept to the proposed method and compared with a similar method and were shown to achieve lower mean-squared error.