Spectral Unmixing With Perturbed Endmembers

• Published in: IEEE transactions on geoscience and remote sensing Vol. 57; no. 1; pp. 194 - 211
• Main Author: Arablouei, Reza
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Abundance; Algorithms; Alternating direction method of multipliers (ADMM); block coordinate-descent (BCD); Computer simulation; Cramer–Rao lower bound (CRLB); Data models; Estimation; Fisher information; Hyperspectral imaging; hyperspectral unmixing; instrumental variable (IV); Libraries; Lower bounds; Manganese; Mathematical analysis; Matrix methods; Mixture models; Objective function; Perturbation methods; perturbed endmembers; Spectra; total least-squares (TLS); total variation
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2018.2852745

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.