Audio signal interpolation using optimal transportation of spectrograms

We present a novel approach for generating an artificial audio signal that interpolates between given source and target sounds. Our approach relies on the computation of Wasserstein barycenters of the source and target spectrograms, followed by phase reconstruction and inversion. In contrast with previous works, our new method considers the spectrograms globally and does not operate on a temporal frame-to-frame basis. Another contribution is to endow the transportation cost matrix with a specific structure that prohibits remote displacements of energy along the time axis, and for which optimal transport is made possible by leveraging the unbalanced transport framework. The proposed cost matrix makes sense from the audio perspective and also allows to reduce the computation load. Results with synthetic musical notes and real environmental sounds illustrate the potential of our novel approach.