Nonlinear Hyperspectral Unmixing Based on Geometric Characteristics of Bilinear Mixture Models

Recently, many nonlinear spectral unmixing algorithms that use various bilinear mixture models (BMMs) have been proposed. However, the high computational complexity and intrinsic collinearity between true endmembers and virtual endmembers considerably decrease these algorithms’ unmixing performances. In this paper, we come up with a novel abundance estimation algorithm based on the BMMs. Motivated by BMMs’ geometric characteristics that are related to collinearity, we conduct a unique nonlinear vertex
${p}$
to replace all the virtual endmembers. Unlike the virtual endmembers, this vertex
${p}$
actually works as an additional true endmember that gives affine representations of pixels with other true endmembers. When the pixels’ normalized barycentric coordinates with respect to true endmembers are obtained, they will be directly projected to be their approximate linear mixture components, which removes the collinearity effectively and enables further linear spectral unmixing. After that, based on the analysis of projection bias, two strategies using the projected gradient algorithm and a traditional linear spectral unmixing algorithm, respectively, are provided to correct the bias and estimate more accurate abundances. The experimental results on simulated and real hyperspectral data show that the proposed algorithm performs better compared with both traditional and state-of-the-art spectral unmixing algorithms. Both the unmixing accuracy and speed have been improved.