Empirical Mode Decomposition-Based Hierarchical Multiresolution Analysis for Suppressing Noise

Abstract

This paper proposes a strategy for suppressing noise via empirical mode decomposition (EMD)-based hierarchical multiresolution analysis. First, an intrinsic mode function (IMF) index that can differentiate the noise-dominant IMFs and the information-dominant IMFs in the first level of decomposition is determined by the conventional EMD-based denoising method. Next, the EMD is applied to those discarded IMFs in the first level of decomposition to obtain the IMFs in the second level of decomposition. Then, the detrended fluctuation analysis (DFA) is employed to define the IMF index separating the noise-dominant IMFs and the information-dominant IMFs in the second level of decomposition. Information-dominant IMFs in both the first and second levels of decompositions are summed together to obtain the denoised signal. The study is limited to signals that were corrupted by additive white Gaussian noise (AWGN). Extensive computer numerical simulations are conducted on both synthetic signals and practical signals. The results show that our proposed method is promising in some cases, especially at high-input SNR levels. For example, in the case of the CH4 signal with 12-dB input SNR, the processed SNR based on our proposed strategy with the consecutive mean squared error (CMSE) is 23.27 dB, while that based on the conventional CMSE method is only 23.14 dB. Also, our proposed method can extract information from more than one level of decomposition to reconstruct the denoised signal compared to only one level of decomposition in the conventional EMD-based denoising method.