Spectral Unmixing With Perturbed Endmembers

We consider the problem of supervised spectral unmixing with a fully-perturbed linear mixture model where the given endmembers, as well as the observations of the spectral image, are subject to perturbation due to noise, error, or model mismatch. We calculate the Fisher information matrix and the Cramer-Rao lower bound associated with the estimation of the abundance matrix in the considered fully-perturbed linear spectral unmixing problem. We develop an algorithm for estimating the abundance matrix by minimizing a constrained and regularized maximum-log-likelihood objective function using the block coordinate-descend iterations and the alternating direction method of multipliers. We analyze the convergence of the proposed algorithm theoretically and perform simulations with real hyperspectral image data sets to evaluate its performance. The simulation results corroborate the efficacy of the proposed algorithm in mitigating the adverse effects of perturbation in the endmembers.