Comment by 331c8c71

I checked your post and it is not clear to me what is the added value of wavelets in the setting you used to illustrate.

The noise was i.i.d. random normal variates with the mean of -0.5 which is exactly like shifting the signal by -0.5 and then adding zero-centered noise. Well, let's say you shift by -10 or -1000 instead - there's no way to recover the magnitude of that shift unless one has additionnal information (like the true signal should be zero mean for instance).