Low-Rank Tensor Modeling of Room Impulse Responses

In this paper, we showcase the benefit of low-rank modeling in the context of acoustic room impulse responses (RIRs). The RIR is modeled as a sum of exponentially decaying sinusoids, and by leveraging the inherent low-rank structure in tensorizations of such signals, we are able to achieve a very compact representation. The contribution of this paper is to provide a clear motivation for the use of low-rank models for the RIR, directly following from physical descriptions of room acoustics. Further, new light is shed on details of the derivation of the RIR model, in relation to solving the inhomogeneous Helmholtz equation. We demonstrate the very compact representations that can be achieved. Finally, the suggested model also displays good robustness properties with respect to the positions of the source and the receiver. Simulations performed on real-life room impulses responses support the theoretical findings.