Can One Hear the Shape of a Room ?

Here is another thought provoking item along the lines of the recent entry Can Compressive Sensing Help the Mapping of Brain Networks ? A while back, I made the case that in the audio business there was not probably a good reason as to why somebody would want to look at changing the recording hardware as you can already get some very high quality ones and even expensive ones. I also wondered what sort of niche market would enable a different sort of microphone that does not just record voice but does something else. Here is the beginning of an answer, a microphone that also does imaging. Here is the first attempt at answering that question: Can One Hear the Shape of a Room: The 2-D Polygonal Case by Ivan Dokmanic, Yue M. Lu and Martin Vetterli. The abstract reads:

We consider the problem of estimating room geometry from the acoustic room impulse response (RIR). Existing attacks on this problem exploit the knowledge of multiple RIRs. In contrast, we are interested in reconstructing the room geometry from a single RIR — a 1–D function of time. We discuss the unicity of the mapping between the geometry of a planar polygonal room and a single RIR. In addition to this theoretical analysis, we also propose an algorithm that performs the “blindfolded” room estimation. Furthermore, the derived results are used to construct an algorithm for localization in a known room using only a single RIR. Verification of the theoretical developments with numerical simulations is given before concluding the paper.