  While the deep learning techniques promote the rapid development of the
speech enhancement (SE) community, most schemes only pursue the performance in
a black-box manner and lack adequate model interpretability. Inspired by
Taylor's approximation theory, we propose an interpretable decoupling-style SE
framework, which disentangles the complex spectrum recovery into two separate
optimization problems \emph{i.e.}, magnitude and complex residual estimation.
Specifically, serving as the 0th-order term in Taylor's series, a filter
network is delicately devised to suppress the noise component only in the
magnitude domain and obtain a coarse spectrum. To refine the phase
distribution, we estimate the sparse complex residual, which is defined as the
difference between target and coarse spectra, and measures the phase gap. In
this study, we formulate the residual component as the combination of various
high-order Taylor terms and propose a lightweight trainable module to replace
the complicated derivative operator between adjacent terms. Finally, following
Taylor's formula, we can reconstruct the target spectrum by the superimposition
between 0th-order and high-order terms. Experimental results on two benchmark
datasets show that our framework achieves state-of-the-art performance over
previous competing baselines in various evaluation metrics. The source code is
available at github.com/Andong-Lispeech/TaylorSENet.
