Removing noise from F2F signal (This question relates to Extracting Binary Magnetic-Strip Card Data from raw WAV)

I am extracting the binary sequence from the magnetic strip on a credit card.



As you can see, the signal is degraded clearly in one place.   also there is a minor degradation right on the left of the image.

Just using IIR (i.e. $X_{\rm out} = 0.9X_{\rm out_{last}} + 0.1X_{\rm in}$) smooths it, but the resulting signal is not mathematically smooth;  if I differentiate the signal a couple of times the noise comes back with a vengeance:



My question is: can I remove the noise in such a way that the derivatives come out clean?

If so, how?

EDIT: Here is a close-up of some damaged waves:



EDIT(2):
A couple of approaches I am considering: 


Firstly I could make a taylor approximation of the signal either side of the damaged sector, and blend the approximations together. 
Secondly I could FFT, remove high-frequency components and reverse FFT. I'm going to try that second approach now...
To remove high-frequency "noise" without removing sharp transitions, you might have to try some sort of non-linear filtering process.

A random example might be applying (cross fading to) a median filter only when the distance to the nearest N local maxima (or minima, and beyond some noise threshold) goes under some distance threshold (where this distance, N and the median filter width, are calibrated to the period of the suspected "noise").