Robust Multi-Pitch Estimation via Optimal Transport Clustering

In this work, we consider the multi-pitch estimation problem, i.e., to estimate multiple sets of harmonically related sinusoids from noisy measurements. We propose to phrase this as a clustering problem with indirect measurements, where we simultaneously infer the spectral content of the signal and group its power into a small set of harmonic structures. The grouping is enforced using a regularization function building on optimal transport theory. The resulting estimator is formulated in terms of the solution of a convex optimization problem, and we present an efficient algorithm implementing the estimator. In numerical experiments, we show that the proposed estimator displays competitive performance as compared to the state-of-the-art. In particular, the proposed estimator is shown to be highly robust to inharmonicities, i.e., deviations from perfect harmonicity.