A Class of Multivariate Denoising Algorithms Based on Synchrosqueezing

Abstract

Univariate thresholding techniques based on high resolution time-frequency algorithms, such as the synchrosqueezing transform, have emerged as important tools in removing noise from real world data. Low cost multichannel sensor technology has highlighted the need for direct multivariate denoising, and to this end, we introduce a class of multivariate denoising techniques based on the synchrosqueezing transform. This is achieved by partitioning the time-frequency domain so as to identify a set of modulated oscillations common to the constituent data channels within multivariate data, and by employing a modified universal threshold in order to remove noise components, while retaining signal components of interest. This principle is used to introduce both the wavelet and Fourier based multivariate synchrosqueezing denoising algorithms. The performance of the proposed multivariate denoising algorithm is illustrated on both synthetic and real world data.