I've tried a few things with the first block of frequency varying noise (vs the time varying spikes), some increasingly random, for example selecting that period of signal and setting it as a noise filter and then applying to the rest of the image to see if it cleaned it up (no surprise there, it didn't). To my mind though that block with varying frequency is intended to convey some form of information and the time varying spikes are intended to convey something as well.
I'm not optimistic about just blindly cleaning up the image, but if they provided a hint as to how to go about it ...