WHY?

Separating multiple sources of audio is difficult task. Previous works mostly made mask for each source in time-fequency domain.

WHAT?

This paper formulated source separation task as getting mixture meight vector of multiple sources in wave form.

$$x(t) = \sum_{i=1}^C s_i(t)\\ x = wB\\ s_i = d_iB\\ w = \sum_{i=1}^C d_i = \sum_{i=1}^C w \odot (d_i \oslash w) := w \odot \sum_{i=1}^C m_i\\ d_i = m_i \odot w$$

Time-domain Audio Separation Network(TasNet) tries to find $m_i$ which is relative contribution to each w while B is N basis signals of shape N x L.

Encoder find w for B by appling 1-D gated convolution layer.

$$w_k = ReLU(x_k \circledast U)\odot\sigma(x_k\circledast V)\\$$

Separation network uses LSTM and FC for masks($m_i$) generation. With w and m found above, d can be found with decoder. The scale-invariant source-to-noise ratio(SI-SNR) is used for loss.

So?

TasNet not only showed comparable performance in WSJ0-2mix dataset, but also showen to find its own basis.

Luo, Yi, and Nima Mesgarani. “Tasnet: time-domain audio separation network for real-time, single-channel speech separation.” 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2018.