A two-step linear mixing model for unmixing under hyperspectral variability

Abstract

Hyperspectral unmixing has been widely used as a technique to interpret hyperspectral data, and to uncover information regarding pure materials and their distribution in an image. A major challenge when unmixing these images is the variability in the spectra of the pure materials (endmembers). Under the linear mixing assumption, several models have been proposed to mitigate this effect, such as the scaled linear mixing model (SLMM) and the extended linear mixing model (ELMM). While the SLMM is often an oversimplified model, leading to significant modeling errors, the ELMM leads to highly nonconvex optimization problems with many non-unique solutions, making it difficult to solve. In this paper, we propose a new two-step linear mixing model (2LMM), which is rich enough to describe hyperspectral variability in a wide variety of cases, while leading to only mildly nonconvex optimization problems that are easier to solve. Using an off-the-shelf interior-point solver, we show that the model performs well and produces better abundance estimates than both the SLMM and ELMM. A MATLAB and Julia demo of the proposed method can be found at github.com/XanderHaijen/two_step_lmm.