## 4 Development of Proposed Method
### Proposed Method
#### 4.2.5 Signal Reconstruction
It is observed that the previous EMD-based method [21] outperforms the rest of the methods, except for a couple of situations. The performance of the previous EMD-based method [21] for experiments with a Blocks signal with an SNR of 0 dB and 20 dB is comparable to that achieved by the EMD-SWT3 [13] and EMD-DFA [11] methods, respectively. The rest of the data-driven denoising methods based on a strict threshold or SWT fall behind the previous EMD-based method [21]. It is worth mentioning that the noticeable performance of the previous method owes to the robust procedure that recovers the signal within the noise-dominant modes, which are in fact rejected as noise in the case of the EMD-DFA [11] and EMD-SC [10] methods. Table 6 presents the MI values obtained from different VMD-based denoising methods for experiments conducted on test signals for various SNR values. It is observed that the proposed VMD-based method appears as the best-performing method, as it yields the highest MI values for all input signals in all experiments. A quick comparison between the results presented in Tables 5 and 6 reveals that the proposed VMD-based method in fact appears as the best-performing method as compared with the rest of the existing EMD-based and VMD-based methods. This demonstrates that the proposed VMD-based method is a promising choice for signal reconstruction tasks, as it consistently outperforms the benchmark methods for various test signals. The effectiveness of the proposed method is further confirmed for real ECG signals as well, as demonstrated by the results presented in the next section. ### Denoising of Real ECG Signals

The results presented in this section demonstrate the denoising performance of the proposed VMD-based method for ECG signals distorted by thermal noise with an SNR of 10 dB. The dataset to conduct simulations is obtained from the Physionet MIT-BIH arrhythmia database (www.physionet.org, accessed on 21 November 2024). The analyzed ECG signals have been specifically taken from recordings labeled 100, 103, 105, 115, and 215. These recordings have been obtained using 11-bit A/D converters and were sampled at a frequency of 360 Hz [30]. As an example, Figure 11 shows raw ECG100 data along with its noisy version obtained by additive wGn with an SNR of 10 dB. Figure 12 displays the results for different ECG signals, where the left column of the subfigures shows the results for the complete span, while the right column shows a zoomed-in version to enhance clarity in the presentation. Here, different time lengths are used for the zoomed-in version of different ECG signals to ensure that at least three cycles are included for each respective signal. The effectiveness of the proposed VMD-based denoising method is demonstrated by the close resemblance between the denoised signal and the clean ECG signal. This is evident from the successful recovery of crucial features, such as peaks and highly varying parts of the signal. Despite the presence of subtle variations, the overall

quality of the denoised signal remains intact. These results validate the usefulness of the denoising technique in reducing sensor noise while preserving previously obscured details. In order to demonstrate the effectiveness of the proposed method in comparison with the existing method, the following methods have been selected for performance comparison: EMD-DFA [11], VMD-DFA [18], and previous EMD-based methods [21]. This choice has been made on the basis of their denoising architecture as well as the results for the test signals. Table 7 presents the overall results from the viewpoints of NMSE (15) and MI (16) for ECG signals considered in the case study. As stated earlier, the best performance scores are denoted in bold, while the second-best values are underlined. The results presented in Table 7 show that the proposed method surpasses the performance of existing methods for all input ECG signals, with the previous EMD-based method [21] appearing as the second-best-performing method.