Abstract:
The primary objective of this project is to develop methods aimed to the conduct the blind signal separation of musical notes with Nonnegative Matrix Factorization (NMF). This is motivated by the fact that music signals are often recorded with a single microphone, hence, there is a need to develop the Automatic Music Transcription (AMT) methods that could mitigate this assumption and produce the desirable separation result. Therefore, this project report presents the rank estimation method for determination of number of musical notes in the recording. It is motivated by the fact that most of the research works on NMF assume \emph{a priori} knowledge regarding the rank of factorization which may not be available in most of the real world scenarios. As a result, the Weighted Singular Value Thresholding based on Stein's Unbiased Risk Estimate (WSVT-SURE) in which rank estimation is performed by non-uniform shrinkage of singular values via weight vector is presented. We also introduce gradient optimization of a smooth approximation of WSVT-SURE (GWSVT-SURE) to estimate the optimal threshold parameter. In the context of AMT, the proposed algorithms allow one to estimate the number of musical note components in the recordings. The proposed algorithms have been evaluated with the polyphonic piano music excerpts. It is observed that the proposed WSVT-SURE algorithm reaches significant improvement in the estimation performance, while GWSVT-SURE shows substantial savings in the computational cost.
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