Is it possible to just remove the noisy part of signal? Is there a way to scan through a signal and remove the parts that don't look "normal". This would mean using more advanced then a simple pass band filter, but something that can look at a period in the signal and remove it if that period didn't fit into a "template".
The short answer is no, unless you know exactly what the noise is, you can not in any practical sense remove the noise. There are things you can do to maximize SNR but no technique exists to remove all noise.