A joint framework for multivariate signal denoising using multivariate empirical mode decomposition

In this paper, a novel multivariate denoising scheme using multivariate empirical mode decomposition (MEMD) is proposed. Unlike previous EMD-based denoising methods, the proposed scheme can align common frequency modes across multiple channels of a multivariate data, thus, facilitating direct multichannel data denoising. The key idea in this work is to extend our earlier MEMD based denoising method for univariate signal in Hao et al. (2016) [19] to the multivariate data. The MEMD modes (known as intrinsic mode functions) for separating noise components are first adaptively selected on the basis of a similarity measure between the probability density function (pdf) of the input multivariate signal and that of each mode by Frobenius norm. The selected modes are then denoised further by a local interval thesholding procedure followed by reconstruction of the thresholded IMFs. The resulting method operates directly in multidimensional space where input signal resides, owing to MEMD, and also benefits from its mode-alignment property. Furthermore, subspace projection is introduced within the framework of the proposed method to exploit the inter-channel dependence among IMFs with the same index, enabling the diversity reception of the signal. Performance of the proposed method against standard multiscale denoising schemes is demonstrated on both synthetic and real world data.