On Spectral Unmixing Resolution Using Extended Support Vector Machines

Due to the limited spatial resolution of multispectral/hyperspectral data, mixed pixels widely exist and various spectral unmixing techniques have been developed for information extraction at the subpixel level in recent years. One of the challenging problems in spectral mixture analysis is how to model the data of a primary class. Given that the within-class spectral variability (WSV) is inevitable, it is more realistic to associate a group of representative spectra with a pure class. The unmixing method using the extended support vector machines (eSVMs) has handled this problem effectively. However, it has simplified WSV in the mixed cases. In this paper, a further development of eSVMs is presented to address two problems in multiple-endmember spectral mixture analysis: 1) one mixed pixel may be unmixed into different fractions (model overlap); and 2) one fraction may correspond to a group of mixed pixels (fraction overlap). Then, spectral unmixing resolution (SUR) is introduced to characterize how finely the mixture in a mixed pixel can be quantified. The quantitative relationship between SUR and WSV of endmembers is derived via a geometry analysis in support vector machine feature space. Thus, the possible SUR can be estimated when multiple endmembers for each class are given. Moreover, if the requirement of SUR is fixed, the acceptance level of WSV is then limited, which can be used as a guide to remove outliers and purify endmembers for each primary class. Experiments are presented to illustrate model and fraction overlap problems and the application of SUR in uncertainty analysis of spectral unmixing.