GBM-Based Unmixing of Hyperspectral Data Using Bound Projected Optimal Gradient Method

Abstract

The generalized bilinear model (GBM) has been widely used for the nonlinear unmixing of hyperspectral images, and traditional GBM solvers include the Bayesian algorithm, the gradient descent algorithm, the semi-nonnegative-matrix-factorization algorithm, etc. However, they suffer from one of the following problems: high computational cost, sensitive to initialization, and the pixelwise algorithm hinders us from applying to large hyperspectral images. In this letter, we apply Nesterov's optimal gradient method to solve the least-square problem under the bound constraint, which is named as the bound projected optimal gradient method (BPOGM). The BPOGM can achieve the optimal convergence rate of $O(1/k^{2})$ , with $k$ denoting the number of iterations in BPOGM. We further apply the BPOGM to solve the GBM-based unmixing problem. Experiments on both synthetic data sets and real hyperspectral images demonstrate that the BPOGM is efficient for solving the GBM-based unmixing problem.