On Spectral Unmixing Resolution UsingExtended Support Vector Machines

Xiaofeng Li, Xiuping Jia, Senior Member, IEEE, Liguo Wang, and Kai Zhao

Abstract—Due to the limited spatial resolution of multispectral/hyperspectral data, mixed pixels widely exist and variousspectral unmixing techniques have been developed for information extraction at the subpixel level in recent years. One of thechallenging problems in spectral mixture analysis is how to modelthe data of a primary class. Given that the within-class spectralvariability (WSV) is inevitable, it is more realistic to associate agroup of representative spectra with a pure class. The unmixingmethod using the extended support vector machines (eSVMs) hashandled this problem effectively. However, it has simplified WSVin the mixed cases. In this paper, a further development of eSVMsis presented to address two problems in multiple-endmemberspectral mixture analysis: 1) one mixed pixel may be unmixedinto different fractions (model overlap); and 2) one fraction maycorrespond to a group of mixed pixels (fraction overlap). Then,spectral unmixing resolution (SUR) is introduced to characterizehow finely the mixture in a mixed pixel can be quantified. Thequantitative relationship between SUR and WSV of endmembersis derived via a geometry analysis in support vector machinefeature space. Thus, the possible SUR can be estimated whenmultiple endmembers for each class are given. Moreover, if therequirement of SUR is fixed, the acceptance level of WSV is thenlimited, which can be used as a guide to remove outliers and purifyendmembers for each primary class. Experiments are presented toillustrate model and fraction overlap problems and the applicationof SUR in uncertainty analysis ofspectral unmixing.
Index Terms—Extended support vector machines (eSVMs),multiple-endmember unmixing, spectral unmixing, spectral unmixing resolution (SUR), support vector machines (SVMs)