Recursive diffeomorphism-based regression for shape functions
© 2018 Society for Industrial and Applied Mathematics. This paper proposes a recursive diffeomorphism-based regression method for the one-dimensional generalized mode decomposition problem that aims at extracting generalized modes αk(t)sk(2πNkφk(t)) from their superpositionKk=1 αk(t)sk(2πNkφk(t)). We assume that the instantaneous information, e.g., αk(t) and Nkφk(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 sk(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.
Xu, J; Yang, H; Daubechies, I
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