Nonlinear Unmixing of Hyperspectral Images via Regularized Wasserstein Dictionary Learning

Hyperspectral images consist of large numbers of pixels across hundreds of spectral bands, making statistical analysis computationally challenging. However, these images often exhibit intrinsic structure that can be leveraged for efficient statistical and machine learning. We propose a novel nonlinear method for unmixing hyperspectral images. In contrast to classical methods which consider an additive linear model, we propose to represent hyperspectral spectra as probability distributions in Wasserstein space and characterize pure spectra as those that allow for typical observations to be reconstructed as entropic Wasserstein barycenters. This allows for the analysis and synthesis of hyperspectral spectra in a geometry-preserving fashion. Results on synthetic data and real HSI show important geometric features of hyperspectral spectra are preserved when utilizing our nonlinear Wasserstein unmixing scheme.