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This paper deals with the problem of the underdetermined blind separation and tracking of moving sources. In practical situations, sound sources such as human speakers can move freely and so blind separation algorithms must be designed to track the temporal changes of the impulse responses. We propose solving this problem through the posterior inference of the parameters in a generative model of an observed multichannel signal, formulated under the assumption of the sparsity of time-frequency components of speech and the continuity of speakers' movements. Specifically, we describe a generative model of mixture signals by incorporating a generative model of a time-varying frequency array response for each source, described using a path-restricted hidden Markov model (H-MM). Each hidden state of the present HMM represents the direction of arrival (DOA) of each source, and so we call it a "DOA-HMM." Through the posterior inference of the overall generative model, we can simultaneously track the DOAs of sources, separate source signals and perform permutation alignment. The experiment showed that the proposed algorithm provided a 6.20 dB improvement compared with the conventional method in terms of the signalto-interference ratio.

We propose a time-domain audio source separation method using down-sampling (DS) and up-sampling (US) layers based on a discrete wavelet transform (DWT). The proposed method is based on one of the state-of-the-art deep neural networks, Wave-U-Net, which successively down-samples and up-samples feature maps. We find that this architecture resembles that of multiresolution analysis, and reveal that the DS layers of Wave-U-Net cause aliasing and may discard information useful for the separation. Although the effects of these problems may be reduced by training, to achieve a more reliable source separation method, we should design DS layers capable of overcoming the problems. With this belief, focusing on the fact that the DWT has an anti-aliasing filter and the perfect reconstruction property, we design the proposed layers. Experiments on music source separation show the efficacy of the proposed method and the importance of simultaneously considering the anti-aliasing filters and the perfect reconstruction property.

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