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What is the important advantage of adopting a wavelet based denosing scheme such as SURE, SUREshrink, etc. than using approaches involving low pass, high pass, band pass, band reject filter for signal denosing?

More precisely, what is the advantage of using wavelet denosing on EEG signals than other methods.

Thank you!

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If you use frequency selective filters for denoising you implicitly assume that the desired signal and the noise occupy different frequency bands. You only remove noise in frequency regions where there is no desired signal, whereas in the passbands of the filter the noise is left unchanged. For some applications the assumption that noise and signal occupy different frequency regions is justified, for some it isn't. Wavelet based denoising methods compose a noisy signal into different scales and attempt to remove the noise while preserving the signal, regardless of the frequency content.

In practice you have to look very carefully at the characteristics of the noise. It is always advisable to apply a frequency selective filter to suppress all out-of-band noise. For narrow band noise sources a notch filter is often sufficient. In cases where you can get a reference signal of the noise (i.e. an independent recording of the actual noise source) the best strategy is using an adaptive noise cancellation algorithm. Only if these more basic methods do not lead to a satisfactory result, and if signal and noise largely overlap in frequency and time, you should look into more sophisticated methods such as wavelet denoising, or blind source separation, which is discussed in the context of your application in this paper.

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