Décomposition de spectres en motifs paramétriques par approximation parcimonieuse

We consider the decomposition of a series of spectra such as those acquired in photoelectron spectroscopy [16]: the data consist of several spectra acquired at different times. The peaks in the spectra are assumed to be Gaussian with positive amplitudes and their characteristics vary slowly between two consecutive spectra. This work aims at estimating the peak parameters and their evolution to help the data interpretation. We propose two original methods based on sparse approximation. In the first method, the spectra are decomposed sequentially with a positivity constraint on the amplitudes using an implementation of the non-negative IRl1 algorithm [19]. In the second approach, we opt for a joint approach with a smooth constraint of the peak positions. In both approaches, the Hungarian algorithm [14] is used to obtain the trajectories of the selected peaks. The proposed methods are compared to a Bayesian approach with RJMCMC [16]: the results are comparable but the calculation time is dramatically reduced.