Publications [#333315] of Ingrid Daubechies

Papers Published

1. Xu, JX; Yang, HY; Daubechies, ID, Recursive Diffeomorphism-Based Regression for Shape Functions, vol. 50 no. 1 (January, 2018), pp. 5-32, Society for Industrial & Applied Mathematics (SIAM) [doi]
   (last updated on 2024/04/17)

   Abstract:
   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.