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arXiv · 1610.03819

Recursive Diffeomorphism-Based Regression for Shape Functions

Jieren Xu·Haizhao Yang·Ingrid Daubechies
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Abstract

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.

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BibTeXRIS

Jieren Xu, Haizhao Yang, Ingrid Daubechies. 2016-10-12. Recursive Diffeomorphism-Based Regression for Shape Functions. https://arxiv.org/abs/1610.03819

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