In underwater acoustics, shallow-water environments act as modal dispersive waveguides when considering low-frequency sources, and propagation can be described by modal theory. In this context, propagated signals are composed of few modal components, each of them propagating according to its own wavenumber. Frequency-wavenumber (f−k) representations are classical methods allowing modal separation. However, they require large horizontal line sensor arrays aligned with the source. In this paper, to reduce the number of sensors, a sparse model is proposed and combined with prior knowledge on the wavenumber physics. The method resorts to a state-of-the-art Bayesian algorithm exploiting a Bernoulli–Gaussian model. The latter, well suited to the sparse representations, makes possible a natural integration of prior information through a wise choice of the Bernoulli parameters. The performance of the method is quantified on simulated data and finally assessed through a successful application on real data.