Bernoulli-Gaussian spectral analysis of unevenly spaced astrophysical data

We address the problem of line spectra detection and estimation from astrophysical data. As observations generally suffer sampling irregularities, false peaks may appear in the Fourier spectrum. We propose a linear spectral model with an arbitrarily large number of fixed frequencies and search for a sparse solution by modelling the spectrum as a Bernoulli-Gaussian process. The use of Markov chain Monte Carlo methods to compute the posterior mean estimate is discussed in the unsupervised framework. The original work by Cheng et al. (1996) is modified to account for specificities of the spectral analysis problem. Simulations reveal the efficiency of the method and its relevance to the astrophysical frequency detection context is emphasized. Finally, an application to astrophysical data is presented.