An empirical wavelet transform based approach for multivariate data processing application to cardiovascular physiological signals

Abstract

Background This article proposes an extension of empirical wavelet transform (EWT) algorithm for multivariate signals specifically applied to cardiovascular physiological signals. Materials and methods EWT is a newly proposed algorithm for extracting the modes in a signal and is based on the design of an adaptive wavelet filter bank. The proposed algorithm finds an optimum signal in the multivariate data set based on mode estimation strategy and then its corresponding spectra is segmented and utilized for extracting the modes across all the channels of the data set. Results The proposed algorithm is able to find the common oscillatory modes within the multivariate data and can be applied for multichannel heterogeneous data analysis having unequal number of samples in different channels. The proposed algorithm was tested on different synthetic multivariate data and a real physiological trivariate data series of electrocardiogram, respiration, and blood pressure to justify its validation. Conclusions In this article, the EWT is extended for multivariate signals and it was demonstrated that the component-wise processing of multivariate data leads to the alignment of common oscillating modes across the components.

Multivariate Variational Mode Decomposition

“…Another important point to highlight in (21) is that a single frequency component ω k is used in the harmonic mixing of the whole vector u k + (t). By design, therefore, we are looking to find multivariate oscillations in u k (t) that have a single common frequency component ω k in all channels.…”

“…However, these extensions inherit all the limitations of standard EMD such as sensitivity to sampling rate, lack of robustness to noise and issues related to the empirical and algorithmic nature of the EMD algorithm. Multivariate extensions for wavelet based methods such as SST [20] and EWT [21] have also emerged recently. The multivariate extension of SST operates by first applying the standard SST algorithm to each channel separately.…”

“…However, individual modes cannot be reconstructed using this approach which limits its applications. The multivariate extension of EWT [21] employs a mode estimation procedure to obtain an optimum signal in the multivariate data set and then segments its corresponding spectra to recover relevant modes across all the channels of input data. The method suffers from inherent flaws of EWT in that it requires explicit construction of adaptive wavelet filters based on spectrum segmentation.…”

“…mode-mixing among different channels of MEMD [23] is also problematic; ii) multivariate extension of SST [20] does not have mode separation capability. It only gives a graphical representation of T-F spectrum thereby limiting its scope of applications to exploratory data analysis only; iii) multivariate extension of EWT [21] is simplistic and relies on predefined boundaries of wavelet filterbank which may be difficult to define in real applications.…”

Noise-Assisted Multivariate Variational Mode Decomposition

“…Thus, multivariate extensions of the univariate data-driven decomposition methods have been proposed, e.g. the multivariate EMD (MEMD) [11,12] and the multivariate VMD (MVDM) [13], among others [14,15,16].…”