  The performance of single channel source separation algorithms has improved
greatly in recent times with the development and deployment of neural networks.
However, many such networks continue to operate on the magnitude spectrogram of
a mixture, and produce an estimate of source magnitude spectrograms, to perform
source separation. In this paper, we interpret these steps as additional neural
network layers and propose an end-to-end source separation network that allows
us to estimate the separated speech waveform by operating directly on the raw
waveform of the mixture. Furthermore, we also propose the use of masking based
end-to-end separation networks that jointly optimize the mask and the latent
representations of the mixture waveforms. These networks show a significant
improvement in separation performance compared to existing architectures in our
experiments. To train these end-to-end models, we investigate the use of
composite cost functions that are derived from objective evaluation metrics as
measured on waveforms. We present subjective listening test results that
demonstrate the improvement attained by using masking based end-to-end networks
and also reveal insights into the performance of these cost functions for
end-to-end source separation.
