Modeling Infrared Spectra: an Algorithm for an Automatic and Simultaneous Analysis

Infrared spectroscopy is a widely used technology for nondestructive testing of materials. We propose a novel approach to automatically and simultaneously analyze a dataset of infrared spectra. They are modeled by linear combinations of peaks whose shape and position are parametrized. The observed data consist of linear combinations of the time-discretized peaks with an additive noise. In order to recover the peak parameters, common to all the dataset, and the associated amplitudes, which are specific to each spectrum, we formulate a penalized non-linear optimization problem. In this context, the penalization ensures that the spectra are recovered using a sparse set of common peaks. Due to the non-convex nature of the problem and the continuous nature of the parameters, a resolution via standard procedures is out of reach. Therefore, we propose an off-the-grid algorithm with alternating convex optimization updates (to estimate the amplitudes of the peaks) and non-convex steps (to estimate the location and the scale of the peaks). In practice, this gives satisfactory results and provides sparse solutions. We also study the numerical performances of the algorithm on simulated data and on real infrared spectra. The latter come from polychloroprene rubbers used in a marine environment at different aging levels. Eventually, we use a clustering algorithm in order to identify the peaks corresponding to the chemical components involved in the aging process of this material.