A number of applications in acoustics, such as echo cancellation, require learning the acoustic impulse response from each deployed loudspeaker to each microphone- the room transfer function. This has conventionally been done separately at each microphone for each loudspeaker. However, the signals arriving at the array share a common structure, which can be exploited to improve the impulse response estimates. In this work, we propose an algorithm that takes advantage of the array structure, as well as the sparsity of the reflections arriving at the array in order to form reliable estimates of the impulse response between each loudspeaker and microphone. The algorithm is shown to improve performance over the matched filter algorithm in echo cancellation applications, using both synthetic and real data.