Empirical Mode Decomposition (EMD) is a data-driven and fully adaptive signal decomposition technique to decompose a signal into its Intrinsic Mode Functions (IMF). EMD has attained great attention due to its capabilities to process a signal in the frequency-time domain without altering the signal into the frequency domain. EMD-based signal denoising techniques have shown great potential to denoise nonlinear and nonstationary signals without compromising the signal’s characteristics. The denoising procedure comprises three steps, i.e., signal decomposition, IMF thresholding, and signal reconstruction. Thresholding is performed to assess which IMFs contain noise. In this study, Interval Thresholding (IT), Iterative Interval Thresholding (IIT), and Clear Iterative Interval Thresholding (CIIT) techniques have been explored for denoising of electromyography (EMG) signals. The effect of different thresholding operators, i.e., SOFT, HARD, and Smoothly Clipped Absolute Deviation (SCAD), on the performance of EMD-based EMG denoising techniques is also investigated. 15 EMG signals, recorded from the upper limb of 5 healthy subjects, were used to identify the best possible combination of thresholding technique and thresholding operator for denoising EMG signals. The performance of denoising techniques is assessed by calculating the Signal to Noise (SNR) ratio of the signals. The results are further evaluated using a two-way Analysis of Variance (ANOVA) statistical test. The results demonstrated that the mean SNR values yielded by the IIT thresholding technique outperform the IT thresholding technique (

The electrophysiological response of motor units from a group of muscles is indicated by electromyography (EMG) recording, a collective electrical manifestation of a contracting muscle. The nervous system controls the motor units generating EMG signals. The recorded EMG, also known as a myoelectric signal, is used for rehabilitation, prosthetic, and clinical diagnostic applications [

The efficacy of the EMG signals may be compromised due to the contamination of the noise. Various frameworks have been proposed to denoise EMG signals. For EMG noise removal, conventional digital filters are the efficient and most straightforward solution [

Huang et al. [

The most crucial step in EMD-based signal denoising techniques is the thresholding of IMFs. After decomposing the original noisy signal into its subsequent IMFs, the task is to identify which IMFs contain noise and portions of the original signal. For the selection of IMFs with noise, the thresholding procedure is applied [

Various studies have already explored the capabilities of EMD-based EMG signal denoising techniques; however, no study has ever investigated the effect of different thresholding methods and thresholding operators on the performance of EMD for the denoising of EMG signals. The main contributions of this study are:

To explore the effect of different thresholding techniques (IT, IIT, and CIIT)

To explore the effect of different thresholding operators (SOFT, HARD, and SCAD), and

To explore the effect of threshold value on the performance of EMD to denoise EMG signals.

The study’s findings will help to select the best possible combination of thresholding operator and thresholding technique for EMD-based EMG denoising technique for enhanced denoising results. Also, the statistical significance of the generated results yielded from EMD-based EMG denoising techniques is reported. In this study, the results are validated using the Analysis of Variance (ANOVA) statistical test and Tuckey’s Honest posthoc test for multiple comparisons. Finally, the best possible combination of thresholding technique and thresholding operator for the denoising of EMG signals based on EMD is proposed to reduce the noise contamination to provide higher SNR substantially.

The rest of the paper is summarized as; the prior knowledge about EMD, thresholding techniques, and the information about the adopted methodology is described in Section 2. The findings of the study are reported in Section 3. Section 4 discusses the results and their statistical significance. The concluding remarks of the study are presented in Section 5.

An adaptive method introduced for analyzing nonstationary and nonlinear signals is Empirical Mode Decomposition (EMD). Theoretically, EMD is similar to Fast Fourier Transform (FFT). However, in FFT, the signal is changed to the frequency spectrum from the time spectrum. The difference between FFT and EMD is that in EMD signal remains in the time domain. It is not assumed to be periodic and decomposed into its Intrinsic Mode Function (IMF). The EMD can be used on different datasets, and no assumptions for the data need to be made. Whereas an IMF is a mono-component function and obeys the following criteria [

Zero crossings and extrema need to be the same or have a difference of one.

At any given point, the local minima envelop, and the mean of the local maxima envelop are zero.

The above-stated criteria restrict an IMF from only a single oscillation per cycle, and each cycle is defined based on the number of zero crossings. Riding waves are not allowed because they can cause negative frequencies, a significant issue in instantaneous frequencies-based applications [

EMD is not a computationally fast method for signal decomposition and suffers from mode mixing [

Wavelet denoising techniques mainly inspire Time-frequency domain denoising techniques. The denoising of digital physiological signals can be elaborated as

Where,

Physiological signals can be denoised using nonparametric signal denoising techniques due to the signals’ nonstationary nature and are inspired by the wavelet denoising technique. In wavelet denoising techniques, a discrete wavelet transform (DWT) of the noisy signal is built by selecting an orthonormal based orthogonal matrix (

Where,

where

By using the SOFT thresholding operator with a threshold equal to

The approximated denoised signal can be modeled as:

The IMF’s resulting from EMD decomposition resembled amplitude and frequency modulated sine waves having a mean equal to zero. Due to this property of IMFs, the direct utilization of thresholding based on wavelet thresholding methods results in discontinuities in the denoised signal. The amplitude of individual IMFs cannot help to determine if the IMF contains noise or the signal. Alternatively, the extrema points can determine if any specific interval of the IMF contains noise or signal. If the IMF contains noise only or if noise is dominated in any IMF, then the extrema value would be below the predefined threshold and vice versa. Utilizing this information, wavelet-based HARD, SOFT, and SCAD thresholding techniques can be translated for EMD as well and can be described by

For j = 1, 2, . . . ,

Just like IT thresholding, IIT is also inspired by the wavelet thresholding technique. In translational invariant wavelet thresholding, various versions of a denoised signal are achieved iteratively. By averaging the various versions of the denoised signals, the iterative process increases the tolerance against noise. IIT works similarly. After IT thresholding, for EMD, various versions of the input signal can be produced. In IIT, this is achieved by decomposition of various noisy forms of the signal under consideration. Various noisy versions of the input signal are achieved by changing the first IMF positions randomly and then combining the first IMF’s noisy version with the remaining IMFs. The following steps are performed in the IIT-based thresholding technique:

Decompose noisy input signal into its N subsequent IMFs using EMD.

Reconstruct the signal, using last N-1 IMFs, without first IMF.

Change the positions of the samples of the first IMF randomly.

Again, reconstruct the signal by adding updated first IMF and signal from step 2.

Again, decompose the newly reconstructed signal using EMD.

Using IT-thresholding, obtain a denoised version of the signal yielded from step 5.

Repeat the procedure M times to obtain M denoised versions of the original signal.

Average the obtained M signals to generate the final denoised version of the signal.

The Clear Iterative Interval Thresholding (CIIT) thresholding technique was designed for low noise and higher SNR value signals. Unlike IIT, in CIIT, the sample of the first IMF’s position is not changed because there is an excellent possibility that the first IMF contains a significant portion of the signal. The useful information is extracted from the first IMF, and any thresholding technique removes the remaining portion. The first IMF’s information is combined with the remaining IMFs to obtain a denoised version of the noisy input signal. The procedure of CIIT is similar to IIT. Only step 2 and 3 of IIT thresholding are changed with the following steps:

Decompose noisy input signal into its subsequent IMFs.

Denoise, the first IMF, using any thresholding technique.

Subtract the denoised version of the first IMF from the original first IMF to obtain its noise-only version.

Reconstruct the signal using all IMFs except the first IMF.

Combine both signals obtained from steps 2 and 4.

Change the position of the samples of the noise-only part of the first IMF.

The EMG dataset is comprised of 15 EMG recordings. Such that 3 EMG signals were recorded from 5 healthy subjects. All the EMG recordings were prerecorded and had been used in [

The recorded EMG signal had a contraction period of 5 s. One second of data from the start and end of the contraction period were discarded to avoid non-stationarity. The remaining data of 3 s was further utilized for signal analysis. To evaluate the efficacy of the investigated signal processing techniques, the recorded EMG signals were first artificially contaminated by introducing synthetically generated random Gaussian noise having different SNR levels in the signals. The noisy EMG signals (

N is a variable with random Gaussian distribution, the SNR levels investigated in this study for noise are

The signal filtration technique’s performance is assessed based on how deliberately the technique could remove noise from the signals and how much information about the original signal is preserved. Signal to noise (SNR) is a widely used performance metric to evaluate the performance of signal filtration techniques and has been used to assess the investigated techniques’ performance. The SNR values are measured before and after the introduction of artificial noise for a fair comparison. The SNR is calculated using

where,

To demonstrate and evaluate the efficacy of EMD for denoising EMG signals, IT, IIT, and CIIT thresholding techniques have been utilized to denoise EMG signals. Along with thresholding techniques, the performance of 3 widely used thresholding operators, i.e., SOFT, HARD, and SCAD, is also investigated. For the said purpose, the EMG signals were used from a prerecorded dataset. A total of 15 EMG signals were used, recorded from 5 healthy subjects. As EMG signals are nonstationary and stochastic, the denoising has been performed on EMG signals with various noise levels. The performance has been measured in terms of SNR before and after denoising of the signals.

The fundamental purpose of EMD is to decompose any given signal into its subsequent IMFs.

The threshold value must always be chosen to be higher than the maximum level of noise in the signal. Donoho and Johnstone [

Subjects | Before | SOFT | HARD | SOFT (T/2) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

IT | IIT | CIIT | IT | IIT | CIIT | IT | IIT | CIIT | ||

1 | 0.00 | 4.04 | 4.24 | 4.18 | 6.27 | 8.16 | 8.12 | 7.18 | 7.64 | 7.63 |

2 | –0.04 | 3.18 | 3.37 | 3.31 | 6.10 | 8.16 | 8.09 | 6.79 | 7.18 | 7.16 |

3 | –0.03 | 3.54 | 3.81 | 3.79 | 6.76 | 8.87 | 8.86 | 7.20 | 7.76 | 7.71 |

4 | –0.04 | 3.67 | 3.97 | 3.90 | 6.78 | 8.70 | 8.66 | 7.26 | 7.70 | 7.69 |

5 | 0.02 | 3.35 | 3.57 | 3.51 | 6.25 | 8.30 | 8.22 | 6.88 | 7.33 | 7.26 |

SNR values of all 3 EMG signals, recorded from each of the five subjects, were averaged to get mean SNR values corresponding to each subject.

Subjects | Before | SOFT | HARD | SCAD | ||||||

IT | IIT | CIIT | IT | IIT | CIIT | IT | IIT | CIIT | ||

SNR 0 dB | ||||||||||

1 | 0.00 | 7.18 | 7.64 | 7.63 | 6.27 | 8.16 | 8.12 | 4.35 | 4.73 | 4.69 |

2 | –0.04 | 6.79 | 7.18 | 7.16 | 6.10 | 8.16 | 8.09 | 3.35 | 3.65 | 3.60 |

3 | –0.03 | 7.20 | 7.76 | 7.71 | 6.76 | 8.87 | 8.86 | 3.76 | 4.31 | 4.22 |

4 | –0.04 | 7.26 | 7.70 | 7.69 | 6.78 | 8.70 | 8.66 | 3.99 | 4.48 | 4.39 |

5 | 0.02 | 6.88 | 7.33 | 7.26 | 6.25 | 8.30 | 8.22 | 3.51 | 3.88 | 3.79 |

SNR 5 dB | ||||||||||

1 | 5.06 | 10.00 | 10.35 | 10.33 | 9.74 | 11.44 | 11.42 | 7.20 | 7.75 | 7.68 |

2 | 4.99 | 9.95 | 10.36 | 10.31 | 10.25 | 12.38 | 12.35 | 6.66 | 7.43 | 7.32 |

3 | 4.99 | 10.51 | 10.94 | 10.90 | 10.98 | 12.91 | 12.86 | 7.45 | 8.20 | 8.18 |

4 | 4.99 | 10.47 | 10.85 | 10.85 | 10.74 | 12.72 | 12.70 | 7.33 | 8.02 | 7.99 |

5 | 5.02 | 9.70 | 10.20 | 10.14 | 10.06 | 12.15 | 12.11 | 6.63 | 7.35 | 7.27 |

SNR 10 dB | ||||||||||

1 | 9.99 | 12.50 | 13.02 | 12.98 | 13.12 | 14.91 | 14.90 | 10.23 | 11.09 | 11.00 |

2 | 10.01 | 13.18 | 13.63 | 13.58 | 14.61 | 16.49 | 16.43 | 10.81 | 11.92 | 11.86 |

3 | 10.00 | 13.81 | 14.20 | 14.17 | 15.13 | 16.87 | 16.92 | 11.62 | 12.71 | 12.59 |

4 | 10.01 | 13.82 | 14.14 | 14.13 | 14.89 | 16.52 | 16.53 | 11.58 | 12.38 | 12.37 |

5 | 10.02 | 12.13 | 12.66 | 12.57 | 13.15 | 14.97 | 14.90 | 10.25 | 11.23 | 11.11 |

SNR 15 dB | ||||||||||

1 | 14.95 | 14.36 | 14.79 | 14.77 | 15.36 | 16.57 | 16.61 | 13.36 | 14.18 | 14.05 |

2 | 14.96 | 14.59 | 15.63 | 15.54 | 15.89 | 18.02 | 17.96 | 13.97 | 15.71 | 15.53 |

3 | 14.96 | 15.50 | 16.39 | 16.23 | 16.88 | 19.12 | 18.89 | 14.78 | 16.19 | 16.16 |

4 | 15.00 | 15.49 | 16.26 | 16.29 | 16.80 | 18.72 | 18.53 | 14.46 | 15.81 | 15.58 |

5 | 14.94 | 13.06 | 13.70 | 13.60 | 14.19 | 15.77 | 15.67 | 12.33 | 13.56 | 13.31 |

SNR values of all 3 EMG signals, recorded from each of the five subjects, were averaged to get mean SNR values corresponding to each subject.

Artificial noise of different SNR levels (0 dB, 5 dB, 10 dB, and 15 dB) was first introduced in the recorded signals to find the optimum thresholding technique for noise removal from EMG signals. The noisy signals were then denoised using IT, IIT, and CIIT thresholding techniques. Results demonstrated that all 3 investigated thresholding techniques significantly remove the noise from signals, irrespective of the level of noise present in the signal. The performance of the thresholding techniques and thresholding operators is shown in

Statistical analysis showed that at 0 dB noise level, there is no statistically significant difference in SNR values between IIT and CIIT thresholding techniques (

Again, when the EMG recordings were contaminated with a 10 dB noise level, the IIT method’s SNR values are statistically significantly different from IT (

From

At a 10 dB noise level, the HARD operator outperformed the other two thresholding operators, and there exists a statistically significant difference among mean SNR values of all thresholding operators (

The study aimed to evaluate the performance of EMD for denoising of EMG signals in the presence of random noise at various levels. It was also intended to evaluate the effect of various thresholding techniques and thresholding operators on the performance of EMD for denoising EMG signals. 15 EMG recordings were used, which were recorded from 5 healthy subjects. All the EMG recordings were first contaminated with noise at various noise levels, and their SNR was calculated. After introducing artificial random noise to original EMG signals, the noisy signals were decomposed using EMD. Various thresholding methods and thresholding operators were then used to denoise the noisy EMG signals. Although EMG signals’ characteristics are very complex and stochastic, the results demonstrate that EMG signals can be successfully denoised using EMD-based denoising techniques.

All three investigated thresholding techniques (IT, IIT, and CIIT) were developed and inspired by wavelet denoising techniques. In wavelet denoising techniques, the selection of threshold value also plays a vital role in denoising signals. Donoho and Johnstone [

To study the effect of different thresholding methods, IT, IIT, and CIIT thresholding techniques were investigated in this study. Results demonstrated that all the investigated thresholding techniques minimized noise in EMG signals when the signals were corrupted with various noise levels. However, the best results are yielded from the IIT thresholding technique for all the investigated EMG recordings corresponding to various noise levels. The IIT and CIIT thresholding technique’s performance is similar, and no statistically significant difference has been observed between IIT and CIIT methods. Originally CIIT was designed and introduced to eliminate noise from signals with low noise levels. However, in the case of EMG signals, it has been observed that for signals corrupted with low or high noise levels, the performance of IIT and CIIT is stable and removes noise from the signals significantly. On all investigated noise levels, two-way ANOVA revealed that the IIT thresholding method outperforms the IT thresholding technique (

To investigate the effect of thresholding operators on the performance of EMD-based denoising technique for denoising of EMG signals, three thresholding operators (SOFT, HARD, and SCAD) have been used in this study. The results demonstrated that for EMG signal denoising HARD thresholding operator provides the best performance results in terms of mean SNR. Individually, at each investigated noise level, the HARD thresholding operator resulted in maximum mean SNR value compared with SOFT and SCAD operators. Whereas combinedly on all investigated noise levels, two-way ANOVA revealed that there is no statistically significant difference in mean SNR values of SOFT and HARD thresholding operator (

This study investigated and explored the efficacy of EMD for denoising of EMG signals at various noise levels. The performance of various thresholding techniques and thresholding operators is also investigated for EMD-based denoising of EMG signals. The results showed that EMG signals could be filtered out, and the effect of noise can be minimized using EMD-based denoising techniques. The performance of IT, IIT, and CIIT thresholding techniques and SOFT, HARD, and SCAD thresholding operator is investigated in this study. It is found that the IIT thresholding technique with HARD thresholding operator yields the best denoising results for EMG signals in terms of SNR, but it fails to preserve the shape of the original signal and produces discontinuities in the denoised EMG signal, irrespective of the noise contamination level of the signals. Whereas IIT with SOFT thresholding operator yields comparatively lower SNR values for denoising EMG signals, it successfully preserves the original signal’s smoothness and characteristics. The inferred results can be used to eliminate the effect of various noise types from EMG signals while preserving the original signal’s characteristics.