Gain estimation approaches in catalog-based single-channel speech-music separation

In this study, we analyze the gain estimation problem of the catalog-based single-channel speech-music separation method, which we proposed previously. In the proposed method, assuming that we know a catalog of the background music, we developed a generative model for the superposed speech and music spectrograms. We represent the speech spectrogram by a Non-Negative Matrix Factorization (NMF) model and the music spectrogram by a conditional Poisson Mixture Model (PMM). In this model, we assume that the background music is generated by repeating and changing the gain of the jingle in the music catalog. Although the separation performance of the proposed method is satisfactory with known gain values, the performance decreases when the gain value of the jingle is unknown and has to be estimated. In this paper, we address the gain estimation problem of the catalog-based method and propose three different approaches to overcome this problem. One of these approaches is to use Gamma Markov Chain (GMC) probabilistic structure to impose the correlation between the gain parameters across the time frames. By using GMC, the gain parameter is estimated more accurately. The other approaches are maximum a posteriori (MAP) and piece-wise constant estimation (PCE) of the gain values. Although all three methods improve the separation performance as compared to the original method itself, GMC approach achieved the best performance.