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Linear spectral unmixing is an effective technique to estimate the abundances of materials present in each hyperspectral image pixel. Recently, sparse-regression-based unmixing approaches have been proposed to tackle this problem. Mostly, l1 norm minimization is used to approximate the l0 norm minimization problem in terms of computational complexity. In this letter, we model the hyperspectral unmixing as a constrained sparse lp - l2(0 <; p <; 1) optimization problem and propose to solve it via the iteratively reweighted least squares algorithm. Experimental results on a series of simulated data sets and a real hyperspectral image demonstrate that the proposed method can achieve performance improvement over the state-of-the-art l1 - l2 method.