Pseudo-Determined Blind Source Separation for Ad-hoc Microphone Networks
We propose a pseudo-determined blind source separation framework that exploits the information from a large number of microphones in an ad-hoc network to extract and enhance sound sources in a reverberant scenario. After compensating for the time offsets and sampling rate mismatch between (asynchronous) signals, we interpret as a determined <inline-formula><tex-math notation="LaTeX">$M\times M$</tex-math></inline-formula> mixture the over-determined <inline-formula><tex-math notation="LaTeX">$M\times N$</tex-math></inline-formula> mixture, where <inline-formula> <tex-math notation="LaTeX">$M>N$</tex-math></inline-formula> is the number of microphones and <inline-formula> <tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of sources. Next, we propose a pseudodetermined mixture model that can apply an <inline-formula><tex-math notation="LaTeX">$M\times M$</tex-math> </inline-formula> independent component analysis (ICA) directly to the <inline-formula><tex-math notation="LaTeX">$M$ </tex-math></inline-formula>-channel recordings. Moreover, we propose a reference-based permutation alignment scheme that aligns the permutation of the ICA outputs and classifies them into target channels, which contain the <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> sources, and nontarget channels, which contain reverberation residuals. Finally, using the signals from nontarget channels, we estimate in each target channel the power spectral density of the noise component that we suppress with a spectral postfilter. Interestingly, we also obtain late-reverberation suppression as by-product. Experiments show that each processing block improves incrementally source separation and that the performance of the proposed pseudodetermined separation improves as the number of microphones increases.