Nonlinear Estimation of Material Abundances in Hyperspectral Images With $\ell_{1}$-Norm Spatial Regularization

Integrating spatial information into hyperspectral unmixing procedures has been shown to have a positive effect on the estimation of fractional abundances due to the inherent spatial-spectral duality in hyperspectral scenes. However, current research works that take spatial information into account are mainly focused on the linear mixing model. In this paper, we investigate how to incorporate spatial correlation into a nonlinear abundance estimation process. A nonlinear unmixing algorithm operating in reproducing kernel Hilbert spaces, coupled with a l
₁
-type spatial regularization, is derived. Experiment results, with both synthetic and real hyperspectral images, illustrate the effectiveness of the proposed scheme.