Hyperspectral abundance estimation for the generalized bilinear model with joint sparsity constraint

In this paper, we present a novel abundance estimation method for the generalized bilinear model (GBM) via sparse representation for hyperspectral imagery. Because the GBM generalizes the linear mixture model (LMM) by introducing an additional bilinear term, our sparsity-based abundance estimation is performed by utilizing two dictionaries-a linear dictionary containing all the pure endmembers and a bilinear dictionary consisting of all the possible bilinear interaction components. Because the components within the bilinear term are also linearly combined, by employing a composite dictionary made up by the concatenation of the linear and bilinear dictionaries we can reformulate the bilinear problem in a linear sparse regression framework. In this way, the abundance values are estimated from the sparse codes only associated with the linear dictionary. To further improve the estimation performance, we incorporate the joint-sparsity model to exploit the spatial information in the data. The experiments demonstrate the effectiveness of the proposed algorithms on both synthetic and real data.