Edited by David L. Donoho, Stanford University, Stanford, CA, and approved May 17, 2013 (received for review January 4, 2013)
Imagine that you are blindfolded inside an unknown room. You snap your fingers and listen to the room’s response. Can you hear the shape of the room? Some people can do it naturally, but can we design computer algorithms that hear rooms? We show how to compute the shape of a convex polyhedral room from its response to a known sound, recorded by a few microphones. Geometric relationships between the arrival times of echoes enable us to “blindfoldedly” estimate the room geometry. This is achieved by exploiting the properties of Euclidean distance matrices. Furthermore, we show that under mild conditions, first-order echoes provide a unique description of convex polyhedral rooms. Our algorithm starts from the recorded impulse responses and proceeds by learning the correct assignment of echoes to walls. In contrast to earlier methods, the proposed algorithm reconstructs the full 3D geometry of the room from a single sound emission, and with an arbitrary geometry of the microphone array. As long as the microphones can hear the echoes, we can position them as we want. Besides answering a basic question about the inverse problem of room acoustics, our results find applications in areas such as architectural acoustics, indoor localization, virtual reality, and audio forensics.
Author contributions: I.D. and M.V. designed research; I.D., R.P., A.W., and Y.M.L. performed research; I.D. and R.P. analyzed data; and I.D. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
*Resonant frequencies correspond to the eigenvalues of a Laplacian on a 2D domain.
†More details about this counterexample are given in the SI Text.
‡Proof is given in SI Text.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1221464110/-/DCSupplemental.
Freely available online through the PNAS open access option.
