Joint Bayesian decomposition of a spectroscopic signal sequence with RJMCMC

Abstract

Abstract-This letter addresses the problem of decomposing a sequence of spectroscopic signals: data are a series of (energy or electromagnetic) spectra and we aim to estimate the peak parameters (centers, amplitudes and widths). The key idea is to perform the decomposition of the whole sequence and to impose the parameters to evolve smoothly through the sequence. The problem is set within a Bayesian framework whose posterior distribution is sampled using a Markov chain Monte Carlo simulated annealing algorithm. Simulations conducted on synthetic data illustrate the performance of the method.

Time-Resolved Observation of the Solvation Dynamics of a Rydberg Excited Molecule Deposited on an Argon Cluster. II. DABCO☆ at Long Time Delays

“…Most informative is the inverted image where several broad bands appear. Their evolution as a function of the time delay τ between the pump and probe pulses is analyzed by the Track Signal Decomposition (TSD) method. ,− This very specific data treatment was already used in Paper I. It helps extracting information from a series of noisy images where the center energy and width of the photoelectron bands vary within the series.…”

Time resolved observation of the solvation dynamics of a Rydberg excited molecule deposited on an argon cluster-I: DABCO☆at short times

“…41 Therefore we use a statistical signal processing approach. 42,43 Each spectrum is modeled as the sum of Gaussian peaks and an added noise (the physical justifications of this model can be found in ref. 13 and 44).…”

“…46 Finally, the estimated decomposition best explains the data with the smallest peak number possible, while favoring tracks with a smooth evolution of their peaks. However, the usual algorithm 42,43 cannot process simultaneously several sequences of spectra, so the P 0 , P 2 and P 4 signals are analysed independently and the solution cannot take into account the specifities of the physics of the relaxation dynamics. Firstly, the decomposition was performed on the P 4 signal which has the lowest number of tracks.…”