Directly measuring the full set of acoustic impulse responses within a room would require an unreasonably large number of measurements. Considering that the acoustic wavefield is sparse in some dictionaries, Compressed Sensing allows the recovery of the full wavefield with a reduced set of measurements, but raises challenging computational and memory issues. Two practical algorithms are presented and compared: one that exploits the structured sparsity of the soundfield, with projections of the modes onto plane waves sharing the same wavenumber, and one that computes a sparse decomposition on a dictionary of independent plane waves with time/space variable separation.