Physiological signal denoising with variational mode decomposition and weighted reconstruction after DWT thresholding

We describe a method for physiological signal denoising based on the variational mode decomposition (VMD), the discrete wavelet transform (DWT), and constrained least squares (CLS) optimization. First, the noisy signal is decomposed into a sum of variational mode functions (VMFs) by VMD. Next, the DWT thresholding technique is applied to each VMF for denoising. Then, a weighted sum of the denoised VMFs is performed after weight estimation by CLS. The summation ignores the residue. This approach is compared to others based on empirical mode decomposition (EMD) and DWT thresholding of the obtained intrinsic mode functions (IMFs) and residue, followed by the unweighted summation of the results. The comparisons were performed with two EEG signals from the left and right cortex of a rat, and one ECG signal from a human subject. Using the signal-to-noise ratio and mean squared error as performance metrics, the results show strong evidence of the superiority of the VMD-DWT-CLS approach over the standard EMD-DWT. It is concluded that using CLS in the final reconstruction stage and ignoring the residue may bring significant improvement to the denoising process.