  This paper proposes a recursive diffeomorphism based regression method for
one-dimensional generalized mode decomposition problem that aims at extracting
generalized modes $\alpha_k(t)s_k(2\pi N_k\phi_k(t))$ from their superposition
$\sum_{k=1}^K \alpha_k(t)s_k(2\pi N_k\phi_k(t))$. First, a one-dimensional
synchrosqueezed transform is applied to estimate instantaneous information,
e.g., $\alpha_k(t)$ and $N_k\phi_k(t)$. Second, a novel approach based on
diffeomorphisms and nonparametric regression is proposed to estimate wave shape
functions $s_k(t)$. These two methods lead to a framework for the generalized
mode decomposition problem under a weak well-separation condition. Numerical
examples of synthetic and real data are provided to demonstrate the fruitful
applications of these methods.
