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

A fast algorithm to find all paths for hyperspectral unmixing

Abundance estimation is one of the most important procedures in spectral unmixing. When the spectral library is fixed, the abundance estimation is to find the optimal subset of the library. This is solved by linear regression with sparsity constraint with nonnegativity i.e. the socalled nonnegative L-1 regression (NNL1). However, it is not clear how to choose the regularisation parameter for a given spectrum to be unmixed. In this paper, a fast algorithm is proposed to find all regularisation paths of NNL1, named as FastNNL1, which selects an optimal result from all paths as the final active set of fractional abundances. The simulation results show that the proposed method performs much better than conventional sparse unmixing algorithms in abundance estimation