Recursive Diffeomorphism-Based Regression for Shape Functions.

This paper proposes a recursive diffeomorphism-based regression method for the 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 Sigma(K)(k)=(1)alpha(k)(t)s(k) (2 pi N-k phi(k)(t)). We assume that the instantaneous information, e.g., alpha(k)(t) and N-k phi(k)(t), is determined by, e.g., a one-dimensional synchrosqueezed transform or some other methods. Our main contribution is to propose a novel approach based on diffeomorphisms and nonparametric regression to estimate wave shape functions s(k)(t). This leads 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 successful application of our approach.