The use of Blind Signal Separation methods (ICA and other approaches) for the analysis of astrophysical data remains quite unexplored. In this paper, we present a new approach for analyzing the infrared emission spectra of interstellar dust, obtained with NASA's Spitzer Space Telescope, using FastICA and Non-negative Matrix Factorization (NMF). Using these two methods, we were able to unveil the source spectra of three different types of carbonaceous nanoparticles present in interstellar space. These spectra can then constitute a basis for the interpretation of the mid-infrared emission spectra of interstellar dust in the Milky Way and nearby galaxies. We also show how to use these extracted spectra to derive the spatial distribution of these nanoparticles.