Flow-Based Independent Vector Analysis for Blind Source Separation

This letter describes a time-varying extension of independent vector analysis (IVA) based on the normalizing flow (NF), called NF-IVA, for determined blind source separation of multichannel audio signals. As in IVA, NF-IVA estimates demixing matrices that transform mixture spectra to source spectra in the complex-valued spatial domain such that the likelihood of those matrices for the mixture spectra is maximized under some non-Gaussian source model. While IVA performs a time-invariant bijective linear transformation, NF-IVA performs a series of time-varying bijective linear transformations (flow blocks) adaptively predicted by neural networks. To regularize such transformations, we introduce a soft volume-preserving (VP) constraint. Given mixture spectra, the parameters of NF-IVA are optimized by gradient descent with backpropagation in an unsupervised manner. Experimental results show that NF-IVA successfully performs speech separation in reverberant environments with different numbers of speakers and microphones and that NF-IVA with the VP constraint outperforms NF-IVA without it, standard IVA with iterative projection, and improved IVA with gradient descent.