Hyperspectral Unmixing With Row-Sparsity Enhancement: A Difference-of-Convex Approach

This paper proposes a new hyperspectral unmixing method that enhances the row sparsity of an abundance matrix via a difference-of-convex (DC) approach. One promising unmixing technique is to promote the row sparsity by designing and solving optimization problems. However, existing methods are unable to both fully enhance the row sparsity and guarantee the convergence of their optimization algorithms, resulting in performance degradation. To address this limitation, we introduce a DC approach to unmixing. First, we design a DC function that promotes the row sparsity while preserving the energies of some row vectors of an abundance matrix. Then, incorporating the DC function, we formulate unmixing as a constrained DC optimization problem. In addition, we develop an algorithm to solve the optimization problem based on the proximal linearized DC algorithm and the preconditioned primal-dual splitting algorithm and guarantee its convergence to a critical point of the problem. Experiments on synthetic and real HS images show that our method is superior to existing methods.