Biomedical Signal Denoising Via Permutating, Thresholding and Averaging Noise Components Obtained from Hierarchical Multiresolution Analysis-Based Empirical Mode Decomposition

Biomedical signals are usually contaminated with interfering noise, which may result in misdiagnosis of diseases. Additive white Gaussian noise (AWGN) is a common interfering noise, and much work has been proposed to suppress AWGN. Recently, hierarchical multiresolution analysis-based empirical mode decomposition (EMD) denoising method is proposed and shows potential performance. In order to further improve performance of hierarchical multiresolution analysis-based EMD denoising, this paper combines hierarchical multiresolution analysis-based EMD, thresholding operation and averaging operation together. In particular, EMD is applied to the first intrinsic mode function (IMF) in the first level of decomposition to obtain IMFs in the second level of decomposition. The first IMF in the second level of decomposition is chosen as the noise component. For each realization, this noise component is segmented into various pieces, and these segments are permutated. By summing up this permutated IMF to the rest of IMFs in both the first level of decomposition and the second level of decomposition, new realization of the noisy signal is obtained. Next, for original signal and each realization of newly generated noisy signal, EMD is performed again. IMFs in the first level of decomposition are obtained. Then, consecutive mean squared errors-based criterion is used to classify IMFs in the first level of decomposition into the information group of IMFs or the noise group of IMFs. Next, EMD is applied to IMFs in the noise group in the first level of decomposition and IMFs in the second level of decomposition are obtained. Detrended fluctuation analysis is used to classify IMFs in the second level of decomposition into the information group of IMFs or the noise group of IMFs. After that, thresholding is applied to IMFs in the noise group in the second level of the decomposition to obtain denoised signal. Finally, the above procedures are repeated, and several realizations of denoised signals are obtained. Then, denoised signal obtained by applying thresholding to each realization is averaged together to obtain final denoised signal. The extensive numerical simulations are conducted and the results show that our proposed method outperforms existing EMD-based denoising methods.