## 3 A Survey on Wavelet Transform-based EEG Denoising Techniques
### Hybrid Methods with Wavelet Transform  
Recently, researchers have been hybridizing the wavelet transform with other efficient denoising techniques. For handling the EEG artifacts, independent component analysis (ICA) is widely employed with wavelet transform [25; 26; 27; 28]. ICA is a mathematical model that decomposes multivariate signals into their subcomponents [29]. In the wavelet-ICA-based method, the input EEG signals are decomposed into wavelet coefficients. Next, all the coefficients are used in ICA operation to separate the various sources of EEG in the time-frequency domain. Then, the artifacted independent components (ICs) are directly eliminated. Finally, all ICs are used in inverse operation followed by inverse wavelet transform to obtain the noise-free EEG signals. [PERSON] et al. [25] provide an example ofcombining wavelet soft-thresholding, whitening method for preprocessing, and ICA for the removal of EMG and ECG artifacts. While [PERSON] et al. proposed a methodology for a wavelet transform-ICA hybrid, [PERSON] et al. [26] showed that using the wavelet transform as an integral part in the separation processes with ICA outperforms hybrid methods that used the wavelet transform as a denoising technique either pre- or post-ICA.  
However, direct elimination of ICs may result in huge information loss as artifacted ICs also contain cerebral activities. [PERSON] et al. [27] modified the wavelet ICA algorithms and instead of direct elimination of artifacted ICs in wavelet domain, they performed thresholding on artifacted ICs to maintain the cerebral activities in ICs. [PERSON] et al. [28] introduced increased automation by implementing a fuzz-kernel support vector machine for identifying artifacts, prior to removal using a wavelet-ICA combination. A basic flow chart of wavelet-ICA is shown in Figure 5. Later on, [PERSON] et al. [30] proposed an unsupervised machine-learning-based method combined with Wavelet-ICA to remove EEG artifacts. They also proposed that the techniques that rely on some arbitrarily defined threshold often fail to accurately identify the signal artifacts in a given dataset.  
However, wavelet transform is limited to single-channel EEG signals. It may perform well for multi-channel EEG signals with the cost of higher computational time and higher computational complexity as performing a wavelet transform channel by channel is a laborious process. To overcome the issue with performing the wavelet transform for multi-channel EEG, a new hybrid method, ICA-wavelet, was developed in the literature [31, 32]. In the ICA-wavelet-based methods, the multi-channel EEG signals were used in ICA to decompose into ICs. Then, artifacted ICs are identified and decomposed into wavelet coefficients. Wavelet coefficients are then thresholded using a universal threshold or a statistical threshold with a hard or soft thresholding function. Finally, clean multi-channel EEG signals are achieved by performing inverse operation of wavelet transform followed by ICA. A basic flow chart of ICA-wavelet based method is shown in Figure 6.  
Figure 5: Basic flow chart of wavelet-ICA based EEG denoising.  
Figure 6: ICA-wavelet-based EEG denoising.