  Self-supervised learning (SSL) representation for speech has achieved
state-of-the-art (SOTA) performance on several downstream tasks. However, there
remains room for improvement in speech enhancement (SE) tasks. In this study,
we used a cross-domain feature to solve the problem that SSL embeddings may
lack fine-grained information to regenerate speech signals. By integrating the
SSL representation and spectrogram, the result can be significantly boosted. We
further study the relationship between the noise robustness of SSL
representation via clean-noisy distance (CN distance) and the layer importance
for SE. Consequently, we found that SSL representations with lower noise
robustness are more important. Furthermore, our experiments on the VCTK-DEMAND
dataset demonstrated that fine-tuning an SSL representation with an SE model
can outperform the SOTA SSL-based SE methods in PESQ, CSIG and COVL without
invoking complicated network architectures. In later experiments, the CN
distance in SSL embeddings was observed to increase after fine-tuning. These
results verify our expectations and may help design SE-related SSL training in
the future.
