  Monaural source separation is important for many real world applications. It
is challenging because, with only a single channel of information available,
without any constraints, an infinite number of solutions are possible. In this
paper, we explore joint optimization of masking functions and deep recurrent
neural networks for monaural source separation tasks, including monaural speech
separation, monaural singing voice separation, and speech denoising. The joint
optimization of the deep recurrent neural networks with an extra masking layer
enforces a reconstruction constraint. Moreover, we explore a discriminative
criterion for training neural networks to further enhance the separation
performance. We evaluate the proposed system on the TSP, MIR-1K, and TIMIT
datasets for speech separation, singing voice separation, and speech denoising
tasks, respectively. Our approaches achieve 2.30--4.98 dB SDR gain compared to
NMF models in the speech separation task, 2.30--2.48 dB GNSDR gain and
4.32--5.42 dB GSIR gain compared to existing models in the singing voice
separation task, and outperform NMF and DNN baselines in the speech denoising
task.
