Recursive Diffeomorphism-Based Regression for Shape Functions

This paper proposes a recursive diffeomorphism based regression method for onedimensional generalized mode decomposition problem that aims at extracting generalized modes αk(t)sk(2πNkφk(t)) from their superposition ∑K k=1 αk(t)sk(2πNkφk(t)). First, a one-dimensional synchrosqueezed transform is applied to estimate instantaneous information, e.g., αk(t) and Nkφk(t). Second, a novel approach based on diffeomorphisms and nonparametric regression is proposed to estimate wave shape functions sk(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.