Development of a Network-Based Method for Unmixing of Hyperspectral Data

This paper presents a new nonlinear unmixing method. Based on relative distances which imply nonlinearity, the method introduces the “fractional distance” as a key variable that quantifies interactions between pixels and endmembers. Relationships between fractional distances and abundance fractions are built through networks. Because an equal spectral mixture of ground spectral classes present on the surface sensed is likely impossible, the proposed method, due to its mathematical concept, reveals unknown endmembers. Three versions of the method have been developed: the nonconstrained, the sum-to-one, and the fully constrained versions. Evaluation of the method using synthetic and real data showed that the method is robust with clear and interpretable results and provides reliable abundance fractions, particularly the sum-to-one and the fully constrained versions of the method. The new unmixing method has also been compared with the fully constrained least squares method.