On the mode synthesis in the synchrosqueezing method

The synchrosqueezing is a powerful tool to analyse and represent multicomponent signals in the time-frequency plane, but the method does not provide a complete and accurate mode decomposition. This paper investigates the modes synthesis issue for a multicomponent signal from selected coefficients of its wavelet transform. We first discuss the reconstruction method proposed by Brevdo et al. to find the wavelet coefficients of a mode and propose an alternative which appears to be more stable. We then remark that the classical synthesis formula from selected wavelet coefficients is not mathematically sound, therefore we propose a new one based on the projection of the coefficients onto some reproducing kernel space. Numerical experiments show the efficiency of our approach for a large range of applications.