Minerals detection over large volume of spectra is the challenge addressed by current hyperspectral imaging spectrometer in Planetary Science. Instruments such OMEGA (Mars Express), CRISM (Mars Reconnaissance Orbiter), M-3 (Chandrayaan-1), VIRTIS (Rosetta) and many more, have been producing very large datasets since one decade. We propose here a fast supervised detection algorithm called LinMin, in the framework of linear unmixing, with innovative arrangement in order to treat non-linear cases due to radiative transfer in both atmosphere and surface. We use reference laboratory and synthetic spectral library. Additional spectra are used in order to mimic the effect of Martian aerosols, grain size, and observation geometry discrepancies between reference and observed spectra. The proposed algorithm estimates the uncertainty on "mixing coefficient" from the uncertainty of observed spectra. Both numerical and observational tests validate the approach. Fast parallel implementation of the best algorithm (IPLS) on Graphics Processing Units (GPU) allows to significantly reduce the computation cost by a factor of similar to 40. (C) 2014 Elsevier Inc. All rights reserved.