Generalized iterative adaptive approach for spectrum estimation based on variational Bayesian inference

Iterative adaptive approach (IAA) which attracted significant interest as a sparse learning method in recent years has find many applications such as spectrum estimation, source location, MIMO imaging and wideband detection, etc. However, the applications of IAA in practice typically require discretizing continuous parameter space by grid to form the sparse representation basis, which is not only the source of heavy computation burden for large problems, but also degrades the accuracy of estimation and restricts the sparsity that could be achieved. It was demonstrated in this paper that IAA could be derived as a special case of the well known Variational Bayesian Inference algorithm under appropriate probabilistic model and assumptions. In addition, a generalized IAA method was proposed to deal with continuous parameters and eliminate the necessity of discretization, which achieve better estimation accuracy and sparsity as shown in numerical simulations.