Recursive Diffeomorphism-Based Regression for Shape Functions
This work addresses mode decomposition for signal processing, but it appears incremental as it builds on existing transforms and regression techniques.
The paper tackles the one-dimensional generalized mode decomposition problem by proposing a recursive diffeomorphism-based regression method to extract generalized modes from their superposition, achieving a framework that works under a weak well-separation condition and demonstrating applications with synthetic and real data.
This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes $α_k(t)s_k(2πN_kφ_k(t))$ from their superposition $\sum_{k=1}^K α_k(t)s_k(2πN_kφ_k(t))$. First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., $α_k(t)$ and $N_kφ_k(t)$. 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.