  This paper investigates different trade-offs between the number of model
parameters and enhanced speech qualities by employing several deep
tensor-to-vector regression models for speech enhancement. We find that a
hybrid architecture, namely CNN-TT, is capable of maintaining a good quality
performance with a reduced model parameter size. CNN-TT is composed of several
convolutional layers at the bottom for feature extraction to improve speech
quality and a tensor-train (TT) output layer on the top to reduce model
parameters. We first derive a new upper bound on the generalization power of
the convolutional neural network (CNN) based vector-to-vector regression
models. Then, we provide experimental evidence on the Edinburgh noisy speech
corpus to demonstrate that, in single-channel speech enhancement, CNN
outperforms DNN at the expense of a small increment of model sizes. Besides,
CNN-TT slightly outperforms the CNN counterpart by utilizing only 32\% of the
CNN model parameters. Besides, further performance improvement can be attained
if the number of CNN-TT parameters is increased to 44\% of the CNN model size.
Finally, our experiments of multi-channel speech enhancement on a simulated
noisy WSJ0 corpus demonstrate that our proposed hybrid CNN-TT architecture
achieves better results than both DNN and CNN models in terms of
better-enhanced speech qualities and smaller parameter sizes.
