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Publications [#333315] of Ingrid Daubechies

Papers Published

  1. Xu, J; Yang, H; Daubechies, I, Recursive Diffeomorphism-Based Regression for Shape Functions, Siam Journal on Mathematical Analysis, vol. 50 no. 1 (January, 2018), pp. 5-32, Society for Industrial & Applied Mathematics (SIAM) [doi]
    (last updated on 2019/04/18)

    Abstract:
    © 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 α k (t)s k (2πN k φ k (t)) from their superposition K k =1 α k (t)s k (2πN k φ k (t)). We assume that the instantaneous information, e.g., α k (t) and N k φ 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.

 

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