Wave re-construction - What are my mathematical options While my question applies to both DSP and Math, I feel it has more depth in mathematics. Here is a sample photo of some samples I have captured over time. 
About the data:
I have a sensor that monitors pressure. When the pressure increases, the y axis value increases. The opposite is true when the pressure decreases. At times however, if the sensor is bent, it can give odd readings ( samples 210 - 300 below ). Hence, the expansion and contraction of pressure is still recorded, but hidden in the noise generated by bending the sensor.

I would like to, mathematically, re-construct the middle of the wave ( between samples 210 to 300ish ) , to be more like the clean wave portions ( 50 - 199, 350-450, etc. ), but remain mathematically correct.
Questions::
My mathematical background in this is very poor. What are some topics I can visit to try and solve my problem? Surely, my problem here is not by any means new. I am just lacking the correct phrasing to really find the topics myself.

The Fourier transform is not a good choice for wave dynamics insofar as they intrinsically nonlinear. Rather, what you need is a method that embraces the non-linearity. Such a method is the Hilbert–Huang transform, which was originally developed specifically for the study of wave motion. It's been some years since I've used this but there are various software available. At that time I used programs that were written in Matlab.
