Sensitivity of Spectral Unmixing Analysis to a Spectrally Dependent Gain Error in Hyperspectral Data

In support of phase a work on the proposed hyperspectral environment and resource observer (HERO) mission, the sensitivity of the results obtained from a common hyperspectral analysis technique, linear spectral unmixing, to a spectrally dependent error in the radiometric calibration of the hyperspectral data is investigated. Two ground-based mineral reflectance spectra are selected as spectral endmembers and combined linearly to give five different mixtures. The MODTRAN atmospheric correction model, as implemented in the imaging spectrometer data analysis system (ISDAS), is used to convert these ground-based reflectance spectra to top-of- atmosphere (TOA) radiance. The resulting mixed spectra are then subjected to a randomly generated spectral gain error (SGE). This is repeated a statistically significant number of times to produce a simulated dataset for each of the five mineral combinations. By varying the magnitude of the introduced SGE, several simulated datasets are produced representing different levels of relative calibration accuracies in the spectral domain. The simulated TOA data sets are then converted back to ground-based reflectance, once again using MODTRAN. Linear constrained spectral unmixing is then applied to each of the simulated datasets. Each of the original mixtures results in a distribution of fractions, the width of which is dependent on the magnitude of the SGE applied to the data set providing the relationship between the unmixing error and the SGE. A specification of the acceptable error in the unmixing results then dictates the required level of accuracy in the spectral gain calibration. The relationship between the SGE and the error in the unmixing results is shown to be directly proportional.