Inverse Filter Circuit
Filtering inverse to a first-order lowpass is very simple:

Lowpass: H1(s)=1/(1+sRC)

Inverse: H2=1+sRC

The inverse filter can be realized with an opamp and R-C-feedback (R between output and inv. input, C between inv. input and ground). The non-inv. opamp input terminal is used for signal input. 

In case o f a second-order lowpass a third quadratic term (s²T²) must be added (second-order differentiator).