Low-Rank Representation of Both Singing Voice and Music Accompaniment Via Learned Dictionaries

Recent research work has shown that the magnitude spectrogram of a song can be considered as a superposition of a low-rank component and a sparse component, which appear to correspond to the instrumental part and the vocal part of the song, respectively. Based on this observation, one can separate singing voice from the background music. However, the quality of such separation might be limited, because the vocal part of a song can sometimes be lowrank as well. Therefore, we propose to learn the subspace structures of vocal and instrumental sounds from a collection of clean signals first, and then compute the low-rank representations of both the vocal and instrumental parts of a song based on the learned subspaces. Specifically, we use online dictionary learning to learn the subspaces, and propose a new algorithm called multiple low-rank representation (MLRR) to decompose a magnitude spectrogram into two low-rank matrices. Our approach is flexible in that the subspaces of singing voice and music accompaniment are both learned from data. Evaluation on the MIR-1K dataset shows that the approach improves the source-to-distortion ratio (SDR) and the source-to-interference ratio (SIR), but not the source-to-artifact ratio (SAR).