Recursive Diffeomorphism-Based Regression for Shape Functions
  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. 
Jieren Xu and Haizhao Yang and Ingrid Daubechies
math.NA cs.CV math.ST stat.TH