Optimal Transport Based Impulse Response Interpolation in the Presence of Calibration Errors

Acoustic impulse responses (IRs) are widely used to model sound propagation between two points in space. Being a point-to-point description, IRs are generally estimated based on input-output pairs for source and sensor positions of interest. Alternatively, the IR at an arbitrary location in space may be constructed based on interpolation techniques, thus alleviating the need of densely sampling the space. The resulting IR interpolation problem is of general interest, e.g., for imaging of subsurface structures based on seismic waves, rendering of audio and radar IRs, as well as for numerous spatial audio applications. A commonly used model represents the acoustic reflections as image sources, often being determined using a sparse reconstruction framework employing spatial dictionaries. However, in the presence of calibration errors, such spatial dictionaries tend to inaccurately represent the actual propagation, limiting the use of these methods in practical applications. Instead of explicitly assuming an image source model, we here introduce a trade-off between minimizing the distance to an image source model and fitting the data by means of a multi-marginal optimal transport problem. The proposed method is evaluated on the early part of real acoustic IRs from the MeshRIR data set, illustrating its preferable performance as compared to state-of-the-art spatial dictionary-based IR interpolation approaches.