A dynamic programming variant of non-negative matrix deconvolution for the transcription of struck string instruments

Given a musical audio recording, the goal of music transcription is to determine a score-like representation of the piece underlying the recording. Most current transcription methods employ variants of non-negative matrix factorization (NMF), which often fails to robustly model instruments producing non-stationary sounds. Using entire time-frequency patterns to represent sounds, non-negative matrix deconvolution (NMD) can capture certain types of non-stationary behavior but is only applicable if all sounds have the same length. In this paper, we present a novel method that combines the non-stationarity modeling capabilities available with NMD with the variable note lengths possible with NMF. Identifying frames in NMD patterns with states in a dynamical system, our method iteratively generates sound-object candidates separately for each pitch, which are then combined in a global optimization. We demonstrate the transcription capabilities of our method using piano pieces assuming the availability of single note recordings as training data.