  Mid-infrared astronomy (operating at wavelengths ranging from 2 to 25 $\mu$m)
has progressed significantly in the last decades, thanks to the improvement of
detector techniques and the growing diameter of telescopes. Space observatories
benefit from the absence of atmospheric absorption, allowing to reach the very
high sensitivities needed to perform 3D hyperspectral observations, but
telescopes are limited in diameter ($< 1$ meter) and therefore provide
observations at low angular resolution (typically a few seconds of arc). On the
other hand, ground-based facilities suffer from strong atmospheric absorption
but use large telescopes (above 8m diameter) to perform sub-arcsecond angular
resolution imaging through selected windows in the mid-infrared range. In this
Paper, we present a method based on Lee and Seung's Non-negative Matrix
Factorization (NMF) to merge data from space and ground based mid-infrared
(mid-IR) telescopes in order to combine the best sensitivity, spectral coverage
and angular resolution. We prove the efficiency of this technique when applied
to real mid-IR astronomical data. We suggest that this method can be applied to
any combination of low and high spatial resolution positive hyperspectral
datasets, as long as the spectral variety of the data allows decomposition into
components using NMF.
