Audio Source Separation in Reverberant Environments Using $\beta$-Divergence-Based Nonnegative Factorization

Gaussian Modeling-Based Multichannel Audio Source Separation Exploiting Generic Source Spectral Model

“…When more recording channels are available thanks to the use of multiple microphones, a multichannel source separation algorithm should be considered as it allows to exploit important information about the spatial locations of audio sources. Such spatial information is reflected in the mixing process (usually with reverberation), and can be modeled by e.g., the interchannel time difference (ITD) and interchannel intensity difference (IID) [26]- [29], the rank-1 time-invariant mixing vector in the frequency domain when following the narrowband assumption [30]- [33], or the full-rank spatial covariance matrix in local Gaussian model (LGM) where the narrowband assumption is relaxed [34]- [36].…”

“…In this paper, we present an extension of the previous works [15], [16], [18] to the multichannel case where the NMF-based GSSM is combined with the full-rank spatial covariance model in a Gaussian modeling paradigm. Around this LGM, existing works have investigated several source spectral models such as Gaussian mixture model (GMM) [37], NMF as a linear model with nonnegativity constraints [36], [38], continuity model [39], kernel additive model [40], heavy-tailed distributionsbased model [41], [42], and recently DNN [24]. Focusing on NMF in this study, our work is most closely related to [38] and [36] as both of them use NMF within the LGM to constrain the source spectra in each EM iteration.…”

“…Around this LGM, existing works have investigated several source spectral models such as Gaussian mixture model (GMM) [37], NMF as a linear model with nonnegativity constraints [36], [38], continuity model [39], kernel additive model [40], heavy-tailed distributionsbased model [41], [42], and recently DNN [24]. Focusing on NMF in this study, our work is most closely related to [38] and [36] as both of them use NMF within the LGM to constrain the source spectra in each EM iteration. However, our work is different from [38] in the sense that we use the pre-trained GSSM, so that potentially the algorithm is less sensitive to the parameter initialization, and it does not suffer from the wellknown permutation problem.…”

“…However, our work is different from [38] in the sense that we use the pre-trained GSSM, so that potentially the algorithm is less sensitive to the parameter initialization, and it does not suffer from the wellknown permutation problem. Our work is also different from [36] as we exploit the mixed group sparsity constraint to guide the optimization, which allows the algorithm to automatically select the most representative spectral components in the GSSM. In addition, instead of constraining the variances of each source by NMF as done in [36], [38], we propose to constrain the total variances of all sources altogether by NMF and show that this novel optimization criterion offers better source separation performance.…”

“…Our work is also different from [36] as we exploit the mixed group sparsity constraint to guide the optimization, which allows the algorithm to automatically select the most representative spectral components in the GSSM. In addition, instead of constraining the variances of each source by NMF as done in [36], [38], we propose to constrain the total variances of all sources altogether by NMF and show that this novel optimization criterion offers better source separation performance. While part of the work was presented in [43], this paper provides more details regarding the algorithm derivation and the parameter settings.…”