Spectral Analysis of Irregularly Sampled Data Using a Bernoulli-Gaussian Model with Free Frequencies

Line spectra estimation is addressed for irregularly sampled astrophysical data. A formulation with a large number of discretized frequencies is used and sparseness is encouraged via a Bernoulli-Gaussian (BG) model on the corresponding amplitudes. Contrary to classic BG models, here the frequency parameters are not constrained on a fixed grid, theoretically enabling unlimited frequency precision. We propose a posterior mean unsupervised estimation scheme combined with an hybrid MCMC algorithm, that allows us to derive crucial information in an astrophysical context, such as confidence levels and variances for each detected spectral line. Simulations confirm the validity of this model with satisfactory estimation results, in addition to a more solid behaviour than parametric methods towards classic astrophysical perturbations