  Sparse signal recovery algorithms like sparse Bayesian learning work well but
the complexity quickly grows when tackling higher dimensional parametric
dictionaries. In this work we propose a novel Bayesian strategy to address the
two dimensional harmonic retrieval problem, through remodeling and
reparameterization of the standard data model. This new model allows us to
introduce a block sparsity structure in a manner that enables a natural pairing
of the parameters in the two dimensions. The numerical simulations demonstrate
that the inference algorithm developed (H-MSBL) does not suffer from source
identifiability issues and is capable of estimating the harmonic components in
challenging scenarios, while maintaining a low computational complexity.
