Each of the images can be decomposed using Wavelets, Contourlets, Curvelets etc. The coefficient matrices/vectors obtained upon decomposition can be treated for minimization of redundancy followed by   application of fusion rule. The fused coefficient matrix can then be reconstructed using the inverse transformation.

The interferogram data from the FTNIR must be fourier transformed into the wavenumber spectrum domain.  Similarly, the data from the NIR hyperspectral imaging are already in the wavenumber domain. 

For classification, if you have a reference wavenumber spectra corresponding to each class type, you can use the Adaptive Cosine Estimator (ACE) or Adaptive Matched Filter (AMF) from open literature to obtain a score for each pixel spectra from both FTNIR and NIR sources.  You can then use a simple fusion rule to decide the aggregate score from the two scores obtained from the FTNIR and NIR sources.

Thank you so much Dr Peng