Impulse Response Interpolation via Optimal Transport

Abstract

Interpolation between multiple room impulse responses is often necessary for dynamic auralization of virtual acoustic environments, in which a listener can move with six degrees-of-freedom. The spatial room impulse response (SRIR) represents the combined effects of the surround room as sound propagates from a source to the listener and varies as the source or listener positions change. The early portion of the SRIR contains sparse reflections, considered to be distinct sound events, that tend to be impaired with interpolation methods based on simple linear combinations. With parametric processing of SRIRs, corresponding sound events are able to be mapped to one another and produce a more physically accurate spatiotemporal interpolation of the early portion of the SRIR.

In this thesis, a novel method for parametric SRIR interpolation is proposed based on the principle of optimal transportation. First, SRIRs are represented as point clouds of sound pressure in a 3D virtual source space. Mappings between two point clouds are obtained by defining a partial optimal transport problem problem, solvable with familiar linear programming techniques. The partial relaxation is implemented by permitting both point-to-point mappings and dummy mappings. The obtained optimal transport plan is used to compute the interpolated point cloud which is converted back to an SRIR.

Testing of the proposed method against three baseline comparison methods was done with SRIRs generated by geometrical acoustical modeling. An error metric based on the difference in energy between low-passed rendering of the omnidirectional room impulse response was used. Statistical results indicate that the proposed method consistently outperforms the baseline methods of interpolation. Qualitative examination of the mapping methods confirms that partial transport produces more physically accurate spatiotemporal mappings. For future work, it is suggested to consider different cost functions, interpolate between measured SRIRs, and to render the responses to allow perceptual tests.