Hyperspectral endmember detection and unmixing based on linear programming

Linear spectral unmixing is a technique to reveal the subpixel information, such as the number of endmembers in the image scene, endmember spectra, and endmember abundance fractions. Many linear spectral unmixing algorithms convert the unmixing problem into constrained linear systems 12]. In this paper, we summarize and classify these algorithms, based on whether the constraints on endmember fractions are considered and whether the priori endmember spectra are required. Then we propose a new linear spectral unmixing algorithm, which is based on linear programming of optimization. The proposed algorithm formulates the linear spectral unmixing as a constrained minimization problem, which includes an objective function and a set of constraint functions. The objective function represents the difference of the image pixel spectra and the computed spectra. By minimizing the objective function while considering the constraints, we obtain an optimal solution to the linear spectral unmixing problem, which represents the endmember fractions. For algorithm validation, we use both simulated hyperspectral data, created from field spectrometer measurements [3] and real hyperspectral data of Hyperion, which were acquired over the Greater Victoria Watershed (GVWD).