Data-Driven Multivariate Signal Denoising Using Mahalanobis Distance

Abstract

A novel multivariate signal denoising method is presented that computes Mahalanobis distance measure at multiple data scales obtained from multivariate empirical mode decomposition (MEMD) algorithm. That enables joint multichannel data denoising directly in multidimensional space $\mathcal {R}^N$ where input signal resides, by employing interval thresholding on multiple data scales in $\mathcal {R}^N$ . We provide theoretical justification of using Mahalanobis distance at multiple scales obtained from MEMD and prove that the proposed method is able to incorporate inherent correlation between multiple data channels in the denoising process. The performance of the proposed method is verified on a range of synthetic and real world signals.