Acoustic Image Source Interpolation with Optimal Transport Barycenter

Room impulse responses can be estimated via the image source model (ISM) using the image source point cloud (ISPC) of a physical source. However, because the source movement changes the ISPC, estimating the ISPC at a new source position typically requires repeated acoustic measurements. We propose an optimal transport (OT) barycenter framework to interpolate the ISPC of a new source location from ISPCs of known sources. The method jointly estimates image-source associations and the ISPC at the new location. The OT ground cost exploits the property that the image sources undergo the same displacement as their physical sources. This approach is realized for both grid-based and support-free configurations. The support-free method addresses the resulting nonconvex joint estimation problem by alternating between identifying image-source associations across the ISPCs and refining the target image-source locations. This enables the interpolation of ISPCs without repeated measurements, facilitating efficient and flexible room-acoustic modeling.