Does thresholding for denoising generally apply to details only?

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Igor 2014-4-10

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https://ww2.mathworks.cn/matlabcentral/answers/125227-does-thresholding-for-denoising-generally-apply-to-details-only

Hello All,

The Wavelet Toolbox graphical interface menu offers two different tools for denoising 1D signals by means of discrete wavelet analysis (without considering SWT and wavelet packets). These are "Wavelet 1-D" and "Wavelet Coefficients Selection 1-D". While the former looks more advanced, it is only the latter that allows selecting approximation coefficients along with detail coefficients for thresholding.

I am wondering why the "Wavelet 1-D" tool does not include an option for selecting/deselecting the approximation coefficients like it is implemented in the "Wavelet Coefficients Selection 1-D" tool.

A more general question: is thresholding only the details enough for noise removal? What are the cases where we would care about thresholding the whole transform (i.e. including the approximations)? It seems to me that when the signal does not oscillate around zero, we'd better keep all the approximation coefficients, as they tend to be (much) higher than the detail coefficients.

Thank you in advance for any thoughts on the topic.