Double Spatial Graph Laplacian Regularization for Sparse Unmixing

Sparse unmixing is an ill-posed inverse problem to find the abundances of each mineral in a scene using a large spectral library. Since the homogeneous regions tend to have similar fractional abundances, including spatial-contextual information increases the performance of an unmixing algorithm. In this letter, we propose a double spatial graph Laplacian regularization for sparse unmixing (DSGLSU). The proposed method consists of two steps. In the first step, hyperspectral data are approximated using a suitable transformation to generate scaled (coarse) data to exploit the interpixel information. Then, a sparsity constrained optimization problem is solved in the approximation domain to produce a coarse abundance matrix. A low-resolution abundance map is obtained by applying an inverse transformation to a coarse abundance map. In the second step, a graph Laplacian and weighted sparsity regularized optimization problem is solved in the original domain to obtain an abundance map where the low-resolution abundance map obtained in the first step is used as a weight term in sparsity regularization. We perform experiments on two simulated data sets and a real data set. It has been shown that the proposed method outperforms the state-of-the-art spatially regularized sparse unmixing methods proposed in the literature.