Reconstruction of the signal produced by a directional sound source from remote multi-microphone recordings

A mathematical method for reconstructing the signal produced by a directional sound source from knowledge of the same signal in the far field, i.e., microphone recordings, is developed. The key idea is to compute inverse filters that compensate for the directional filtering of the signal by the sound source directivity, using a least-square error optimization strategy. Previous work pointed out how the method strongly depends on arrival times of signal in the microphone recordings. Two strategies are used in this paper for calculating the time shifts that are afterward taken as inputs, together with source directivity, for the reconstruction. The method has been tested in a laboratory environment, where ground truth was available, with a Polaroid transducer as source. The reconstructions are similar with both strategies. The performance of the method also depends on source orientation.