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.