Subtracting signals to re-construct the middle
No, you can't restore a low - frequency signal by DFT of its parts due to the periodic DFT nature and because 
$$
IDFT(DFT( \frac{U(t) + V(t)}{2})) == \frac{U(t) + V(t)}{2}
$$
by definition.
You can apply filtering or smoothing to remove the high - frequency noise.