Estimation of the Matrix Rank of Harmonic Components of a Spectrogram in a Piano Music Signal Based on the Stein's Unbiased Risk Estimator and Median Filter

Abstract

The estimation of the matrix rank of harmonic components of a music spectrogram provides some useful information, e.g., the determination of the number of basis vectors of the matrix-factorization-based algorithms, which is required for the automatic music transcription or in post-processing. In this work, we develop an algorithm based on Stein's unbiased risk estimator (SURE) algorithm with the matrix factorization model. The noise variance required for the SURE algorithm is estimated by suppressing the harmonic component via median filtering. An evaluation performed using the MIDI-aligned piano sounds (MAPS) database revealed an average estimation error of -0.26 (standard deviation: 4.4) for the proposed algorithm.