Math @ Duke

Publications [#333315] of Ingrid Daubechies
Papers Published
 Xu, J; Yang, H; Daubechies, I, Recursive DiffeomorphismBased Regression for Shape Functions,
Siam Journal on Mathematical Analysis, vol. 50 no. 1
(January, 2018),
pp. 532, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/02/17)
Abstract: © 2018 Society for Industrial and Applied Mathematics. This paper proposes a recursive diffeomorphismbased regression method for the onedimensional 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 onedimensional 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 wellseparation condition. Numerical examples of synthetic and real data are provided to demonstrate the successful application of our approach.


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