Sparse vector factorization for underdetermined BSS using wrapped-phase GMM and source log-spectral prior

We propose a sparse vector factorization (SVF) approach for blind source separation, which inherently avoids the permutation problem. The SVF assumes the sparseness of sources, and defines a sparse vector (SV) that consists of the locational and spectral features of each source at all the frequencies. Then, by assuming that the locational and spectral SVs are generated by frequency-independent parameters, the method executes the SVF. Our locational feature is the phase difference (PD) between two microphone observations, and we model it with a frequency-independent time-difference of arrival (TDOA) parameter. Moreover, we employ the wrapped-phase GMM in order to take the spatial aliasing problem into account. On the other hand, the spectral feature is the log spectrum, and we provide a prior for a spectral parameter. The SVF is formulated with a maximum a posteriori (MAP) estimation framework, where the locational and spectral parameters are inferred by the EM algorithm. Experimental results show that our proposed method can separate signals successfully even for an underdetermined case.