Consider a sensing system using a large number of N microphones placed in multiple dimensions to monitor a broadband acoustic field. Using all the microphones at once is impractical because of the amount of data generated. Instead, we choose a subset of D microphones to be active. Specifically, we wish to find the set of D microphones that minimizes the largest interference gain at multiple frequencies while monitoring a target of interest. A direct, combinatorial approach -testing all N choose D subsets of microphones -is impractical because of problem size. Instead, we use a convex optimization technique that induces sparsity through a l1-penalty to determine which subset of microphones to use. We test the robustness of the our solution through simulated annealing and compare its performance against a classical beamformer which maximizes SNR. Since switching from a subset of D microphones to another subset of D microphones at every sample is possible, we construct a space-time-frequency sampling scheme that achieves near optimal performance.