Multi-pitch estimation via fast group sparse learning

In this work, we consider the problem of multi-pitch estimation using sparse heuristics and convex modeling. In general, this is a difficult non-linear optimization problem, as the frequencies belonging to one pitch often overlap the frequencies belonging to other pitches, thereby causing ambiguity between pitches with similar frequency content. The problem is further complicated by the fact that the number of pitches is typically not known. In this work, we propose a sparse modeling framework using a generalized chroma representation in order to remove redundancy and lower the dictionary's block-coherency. The found chroma estimates are then used to solve a small convex problem, whereby spectral smoothness is enforced, resulting in the corresponding pitch estimates. Compared with previously published sparse approaches, the resulting algorithm reduces the computational complexity of each iteration, as well as speeding up the overall convergence.