Off-The-Grid Multi-Pitch Estimation Using Optimal Transport

In this work, we address the problem of multi-pitch estimation. Conventional estimators typically rely on predetermined pitch grids. Moreover, most existing methods assume perfect harmonic behavior for the signal, which renders them sensitive to deviations from the harmonic model. This work addresses both problems using an optimal transport framework in combination with a block coordinate descent scheme, alternating between updating the estimate of the spectral content of the signal and the fundamental frequency estimates. The estimates of the proposed method are contingent on an a priori estimate of the fundamental frequencies, herein addressed by the use of an estimator from our previous work. The proposed method shows promising improvements compared to the existing methods, particularly in the case of small deviations in the frequencies of the harmonic model.