To begin with, try to make the example as small as possible. Your problem is demonstrated in the first notebook by this:

Don = {....}
TransfoBis = StationaryWaveletTransform[Don, SymletWavelet[8]];
Filtre = InverseWaveletTransform[TransfoBis];
ListPlot[Don - Filtre, PlotRange -> All]

How small can you make "Don" and still reproduce the problem?

Also, I'm not seeing this issue on my machine. For me, The mean value of the absolute value of the residuals is rather small:

Mean[Abs[Don - Filtre]]

5.06531*10^-14

(1) I would suggest trying to reset Mathematica to its installation default configuration according to this article: http://support.wolfram.com/kb/12464 (2) What OS are you working on?

Unfortunately, the previous version was uninstalled from my PC, but I confirm that I noticed that the obtained results were different after upgrading. In fact, I used Symlets for filtering signals, and, as you can see on the second notebook, the signal filtred with these wavelets is completely different from the signal filtered with Haar wavelets, or Daubechies'. I don't think it's normal; in addition, in the notebook I sent yesterday, we could observe that, in this system, InverseWaveletTransform[StationaryWaveletTransform[data, SymletWavelet[8]]] is totally different from data! It's abnormal, I think...

Attachments:

If I could debug this for you, I would. But, I cannot reproduce the problem. The problem is somehow specific to your computer.

Please:

(1) Create a new, empty notebook.

(2) Put this code in the notebook.

Don = {....}
TransfoBis = StationaryWaveletTransform[Don, SymletWavelet[8]];
Filtre = InverseWaveletTransform[TransfoBis];
ListPlot[Don - Filtre, PlotRange -> All]

(3) Reduce the size of Don as small as possible while showing your problem.

(4) Evaluate the command SystemInformation[] in this notebook. This command produces a dialog with lots of information about your computer and Mathematica installation.

(5) Send an email to Wolfram Technical Support (support@wolfram.com or https://www.wolfram.com/support/contact/email/?topic=Technical). Attach this new notebook to the email. In the email, tell them that InverseWavletTransform doesn't appear to be working correctly on your computer. They will be able to forward your email to someone who will be able to help you.