Linear Spectral Mixing Model for Identifying Potential Missing Endmembers in Spectral Mixture Analysis

A problem that is frequently arising in the spectral mixture analysis is how to correctly identify the endmembers present in the scene. In the analysis of image data covering natural scenes, vegetation, bare soil, and shade/water are commonly assumed as endmembers, but other endmembers may also be present. This paper investigates an approach based on the analysis of residuals produced by the linear spectral mixing model for identifying potential missing endmembers. The basic proposition consists in assuming that larger residuals are caused by missing endmembers. The image is segmented in terms of the residuals, and the Kolmogorov-Smirnov test is applied to group segments that show similar residuals and are thus likely to include the same missing endmember. An approach to estimate the spectral response of the missing endmembers is also investigated. The proposed methodology is tested by using Thematic Mapper Landsat and Coupled Charge Device China-Brazil Earth Resources Satellite image data. In addition to vegetation, bare soil, and shade/water, two additional endmembers were included as missing endmembers (clouds and water bodies with a large load of suspended sediments). The tests have shown that the proposed methodology is capable of detecting image regions that include missing endmembers and of correctly estimating the corresponding spectral responses.