Understanding the impact of spatial resolution in unmixing of hyperspectral images

Abstract

Unmixing is an ill-posed inverse problem and as such the solution computed with different unmixing algorithms depends on the underlying assumptions for the inverse problem. Ideally one would expect similar solutions for unmixing a hyperspectral image of different spatial resolutions of the same scene. In this paper, we study the results of unmixing different images of the same area at different spatial resolution using different unmixing algorithms. We also compare the estimation of the number of endmembers using the rank of a scaled correlation matrix against the positive rank estimated with the fitting error of a positive matrix factorization. The results show that algorithms that assume the pure pixels in the image given consistent results in the same scale and are limited to the number of endmembers determined from the rank of the scaled correlation matrix while algorithms that do not assume pure pixels are consistent across spatial scales and the number of endmembers is better estimated by the positive rank. One and four meter data collected with the AISA sensor over southwestern Puerto Rico is used for the study.