In this paper, we develop a sparsity-aware algorithm for direction-of-arrival (DOA) estimation of correlated targets in the context of coprime array processing. The idea is to iteratively interpolate the observed data to a virtual nonuniform linear array (NLA) in order to raise the degrees of freedom (DOF). We derive the estimation procedures using variational inference for fully Bayesian estimation, where the current parameter estimates are used to interpolate the observed data better and thus increase the likelihood of the next parameter estimates. The novelties of our method lies in its capacity of detecting more correlated sources than the number of physical sensors. Simulated data from coprime arrays are used to illustrate the superior performance of the proposed approach as compared with other state-of-the-art compressed sensing reconstruction algorithms.