The absorption positions and shapes are key information to identify and characterize a mineral from its reflectance spectrum. With the development of new airborne and satellite-borne hyperspectral sensors, automatic methods have to be developed to extract and analyze this useful information. A flexible deconvolution procedure, able to deal with various sensor characteristics and a wide variety of minerals of interest, is proposed. The approach is based on the sparse representation of the spectrum and the use of a greedy algorithm, the Non-Negative Orthogonal Matching Pursuit algorithm. First, NNOMP is adapted to deal with a parameteric physical model of mineral reflectance spectra. Then, noise statistical information is taken into account to improve the detection of small absorptions while minimizing overfitting effects. The procedure is tested on real data from two quarries in France. Results show the potential of our procedure for the estimation of a consistent number of absorptions whose parameters can be used to analyze the mineralogy.