© 2017 IEEE. Sparse representations of sound fields have become popular in various acoustic inverse problems. The simplest models assume spatial sparsity, where a small number of sound sources are located in the near-field. However, the performance of these models deteriorates in the presence of strong reverberation. To properly treat the reverberant components, we introduce three types of reverberation models: a low-rank model, a sparse model in the plane-wave domain, and a combined low-rank+sparse model. We discuss corresponding decomposition algorithms based on ADMM convex optimization. Numerical simulations indicate that the decomposition accuracy is significantly improved by the additive model of low-rank and sparse plane wave models.