Spectral unmixing in the linear mixing model case can be addressed using non-negative matrix factorization (NMF) algorithms. However, NMF algorithms do not yield a unique solution when the data at hand does not satisfy some uniqueness conditions. Therefore, a set of admissible solutions will be found. The main purpose of this paper is to discuss how much a sparse representation of the data matrix can reduce this set of admissible solutions in the case of spectral unmixing. We propose an algorithm allowing to perform efficiently the sparse representation of data matrix under non-negativity constraints and to assess the admissible solutions when the NMF is performed on the sparse data matrix in the case of reflectance hyperspectral imaging data.