We propose to acquire large sets of room impulse responses (RIRs) by simultaneously playing known source signals on multiple loudspeakers. We then estimate the RIRs via a convex optimization algorithm using convex penalties promoting sparsity and/or exponential amplitude envelope. We validate this approach on real-world recordings. The proposed algorithm makes it possible to estimate the RIRs to a reasonable accuracy even when the number of recorded samples is smaller than the number of RIR samples to be estimated, thereby leading to a speedup of the recording process compared to state-of-the-art RIR acquisition techniques. Moreover, the penalty promoting both sparsity and exponential amplitude envelope provides the best results in terms of robustness to the choice of its parameters, thereby consolidating the evidence in favor of sparse regularization for RIR estimation. Finally, the impact of the choice of the emitted signals is analyzed and evaluated.