Weighted Singular Value Thresholding and Gradient Optimization of Unbiased Risk Estimate for Rank Estimation in Automatic Music Transcription

Most of the research works on music transcription assume a priori knowledge regarding the number of musical notes or instruments. This paper proposes two novel algorithms for Automatic Music Transcription (AMT). The first algorithm eploys the Weighted Singular Value Thresholding based on Stein's Unbiased Risk Estimate (WSVT-SURE) and performs note estimation by non-uniform shrinkage of singular values via weight vector. Furthermore, gradient optimization of a smooth approximation of WSVT-SURE (GWSVT-SURE) is proposed to estimate the optimal threshold parameter. The proposed algorithms have been evaluated with the polyphonic piano music excerpts. The proposed algorithms allow one to precisely estimate the number of musical note components in the recordings. It has been observed that the proposed WSVT-SURE algorithm reaches significant improvement in the estimation performance, while the proposed GWSVT-SURE algorithm shows substantial savings in the computational cost.