Reflectance spectroscopy is a widely used technique for mineral identification and characterization. Since modern airborne and satellite-borne sensors yield an increasing number of hyperspectral data, it is crucial to develop unsupervised methods to retrieve relevant spectral features from reflectance spectra. Spectral deconvolution aims to decompose a reflectance spectrum as a sum of a continuum modeling its overall shape and some absorption features. We present a flexible and automatic method able to deal with various minerals. The approach is based on a physical model and allows us to include noise statistics. It consists of three successive steps: (i) continuum pre-estimation based on non-linear least-squares; (ii) pre-estimation of absorption features using a greedy algorithm; (iii) refinement of the continuum and absorption estimates. The procedure is first validated on synthetic spectra, including a sensitivity study to instrumental noise and a comparison to other approaches. Then, it is tested on various laboratory spectra. In most cases, absorption positions are recovered with an accuracy lower than 5 nm, enabling mineral identification. Finally, the proposed method is assessed using hyperspectral images of quarries acquired during a dedicated airborne campaign. Minerals such as calcite and gypsum are accurately identified based on their diagnostic absorption features, including when they are in a mixture. Small changes in the shape of the kaolinite doublet are also detected and could be related to crystallinity or mixtures with other minerals such as gibbsite. The potential of the method to produce mineral maps is also demonstrated.