Unsupervised joint decomposition of a spectroscopic signal sequence

• This work aims at estimating the parameters of Gaussian peaks in spectroscopic signals.
• Data gather actually several spectroscopic signals, so the decomposition is performed jointly on the whole data.
• The peaks evolve slowly through the data and may appear and disappear.
• We propose an original Bayesian model and an implementation of the RJMCMC algorithm.
• The performances of the method are discussed on synthetic and real (photoelectron) data.

This paper addresses the problem of decomposing a sequence of spectroscopic signals. Data are a series of signals modeled as a noisy sum of parametric peaks. We aim to estimate the peak parameters given that they change slowly between two contiguous signals. The key idea is to decompose the whole sequence rather than each signal independently. The problem is set within a Bayesian framework. The peaks with similar evolution are gathered into groups and a Markovian prior on the peak parameters of a same group is used to favor a smooth evolution of the peaks. In addition, the peak number and the group number are unknown and have to be estimated (the number of peaks in two contiguous signals change if peaks vanish). Therefore, the posterior distribution is sampled with a reversible jump Markov chain Monte Carlo algorithm. Simulations conducted on synthetic and real photoelectron data illustrate the performance of the method.