Sparse dictionary learning for blind hyperspectral unmixing

Dictionary learning (DL) has been successfully applied to blind hyperspectral unmixing due to the similarity of underlying mathematical models. Both of them are linear mixture models and quite often sparsity and nonnegativity are incorporated. However, the mainstream sparse DL algorithms are crippled by the difficulty in prespecifying suitable sparsity. To solve this problem, this paper proposes an efficient algorithm to find all paths of the ℓ₁-regularization problem and select the best set of variables for the final abundances estimation. Based on the proposed algorithm, a DL framework is designed for hyperspectral unmixing. Our experimental results indicate that our method performs much better than conventional methods in terms of DL and hyperspectral data reconstruction. More importantly, it alleviates the difficulty of prescribing the sparsity.