Direction of Arrival Based Spatial Covariance Model for Blind Sound Source Separation

Gaussian Model Based Multichannel Separation

“…If there is a certain assumption, constraint or structure that we want to impose on the power spectrum of each source, we can employ a parametric model to represent σ 2 j (n, f ) instead of individually treating σ 2 j (n, f ) as a free parameter, or introduce a properly designed prior distribution over σ 2 j (n, f ). Choices include a Gaussian mixture model (GMM) (Attias, 2003), a hidden Markov model (HMM) (Higuchi and Kameoka, 2015), an autoregressive (AR) model (Déger-ine and Zaïdi, 2004;Yoshioka et al, 2011), a nonnegative matrix/tensor factorization (NMF) model (Ozerov and Févotte, 2010;Arberet et al, 2010;Ozerov et al, 2011;Sawada et al, 2013;Nikunen and Virtanen, 2014;Kitamura et al, 2015), an excitation-filter model (also known as source-filter model) Ozerov et al, 2012), a spectral continuity prior (Duong et al, 2011), a deep neural network (DNN) model (Nugraha et al, 2016), and combinations of different models (Ozerov et al, 2012;Adiloğlu and Vincent, 2016), among others. These models are presented in detail in Section 1.2.1.…”

“…Multichannel source separation methods using this model or its variants are called multichannel NMF (Ozerov and Févotte, 2010;Kameoka et al, 2010;Sawada et al, 2013;Nikunen and Virtanen, 2014;Kitamura et al, 2015). They generalize the single-channel Itakura-Saito (IS) NMF methods reviewed in Chapters ??…”

“…With this model, the entire set of spectral templates is partitioned into subsets associated with individual sources. It is also possible to allow all the spectral templates to be shared by every source and let the contribution of the k-th spectral template to source j be determined in a learning-free manner (Ozerov et al, 2011;Sawada et al, 2013;Nikunen and Virtanen, 2014;Kitamura et al, 2015). To do so, we drop the index j from b jk (f ) and h jk (n), and instead introduce a continuous indicator variable φ jk ≥ 0 such that j φ jk = 1. φ jk can be interpreted as the expectation of a binary indicator variable, describing to which of the J sources the k-th template is assigned.…”

“…Alternatively, Nikunen and Virtanen (2014) consider a DOA grid {α k } K k=1 and constrain the spatial covariance matrix of each source as 45) with nonnegative weights q jk . Such a combination of DOA-based rank-1 models (also called DOA kernels) makes it possible to model not only the direct path, but also reflections.…”

“…Sawada et al (2013) and Nikunen and Virtanen (2014) proposed to replace this measure of fit by the Frobenius norm. This leads to the cost…”