## 3 Brief Overview of EMD-Based Methods  
Figure 1 shows block diagrams for various EMD-based methods. To benchmark the proposed method, the following methods have been selected: EMD with stringent correlation thresholding (EMD-SC) [10], EMD-MI [14], EMD coupled with DFA (EMD-DFA) [11], EMD-SWT3 [13], and the EMD-based previous method [21]. These state-of-the-art methods employ diverse mathematical techniques such as correlation, MI, scaling coefficients, and SWT, and are good candidates to be included in the study presented in this paper. As shown in Figure 1a, EMD-SC employs a correlation-based method to find and get rid of duplicate IMFs [10]. This method assumes that the noise present in the signal is dispersed throughout all of the IMFs. Each IMF would have a reasonably strong correlation with the original signal since the IMFs are thought to be virtually orthogonal components of the original signal; this assumes that the irrelevant components would have a relatively weak correlation with the original signal. IMFs that are strongly associated are merged or removed to create a collection of IMFs that are maximally independent. The correlation threshold is used to determine how similar IMFs are to one another. The procedure entails calculating correlation coefficients between each IMF and the original signal in order to distinguish between important and irrelevant IMFs, particularly when noise-containing signals are taken into account. A threshold is established as a function of the greatest correlation coefficient after decomposing a number of trial signals; only IMFs with correlation coefficients higher than the established threshold are kept. One aspect of EMD-SC is that denoising the signal-dominant IMFs in certain circumstances may result in the loss of part of the information included in the original signal. Figure 1b shows the EMD-MI method where conditional MI is used to detect the cutoff between noise-dominant and signal-dominant modes, as opposed to strict thresholding for partial reconstruction [14]. The statistical link between the IMFs and the original signal may be ascertained using MI, which measures the mutual dependency between two random variables. The obtained IMFs are divided into two groups, with only the noise-dominant group undergoing denoising using [PERSON]'s unbiased risk estimate (SURE) as a shrinkage metric. However, since this technique relies on estimates utilizing the signal and noise qualities, several attempts to fit more suitable estimators have been proposed. Figure 1: Block diagrams for EMD-based benchmark algorithms: (**a**) EMD-SC [10], (**b**) EMD-MI [14], (**c**) EMD-DFA [11], (**d**) EMD-SWT3 [13], and (**e**) EMD-based previous method [21]. (Here, selection/behavior of the thresholding parameter \(\theta\) depends upon the respective method and is discussed in detail in the manuscript). Figure 1c EMD-DFA [11], which has the advanced virtue of being independent of any estimators. In order to discover scaling features and find long-range correlations, DFA can detrend non-stationary time series [22]. The main idea of DFA is to compute the fluctuation graph, \(F(n)\), which represents the average root-mean-square (RMS) of the time series with regard to local trends in the data-dependent box sizes. The scaling exponent \(\alpha\) is linked to the Hurst exponent, which measures the strength of correlation in a time series [23]. This relationship helps measure the persistence or anti-persistence of trends, providing insight into the strength and nature of correlations over time. A score of \(\alpha=0.5\) indicates that the signal is devoid of correlation and is similar to white noise [24]. Consequently, irrelevant IMFs that contain mostly noise can be removed from the observed signal. Figure 1d shows the EMD-SWT3 method for eliminating noise and artifacts by combining SWT (3-level) with EMD [13]. First, the signals are decomposed into various IMFs, and SWT is applied to facilitate noise removal.