Relationships Between Nonlinear and Space-Variant Linear Models in Hyperspectral Image Unmixing

Hyperspectral image unmixing is a source separation problem whose goal is to identify the signatures of the materials present in the imaged scene (called endmembers), and to estimate their proportions (called abundances) in each pixel. Usually, the contributions of each material are assumed to be perfectly represented by a single spectral signature and to add up in a linear way. However, the main two limitations of this model have been identified as nonlinear mixing phenomena and spectral variability, i.e., the intraclass variability of the materials. The former limitation has been addressed by designing nonlinear mixture models, whereas the second can be dealt with by using (usually linear) space varying models. The typical example is a linear mixing model where the sources can vary from one pixel to the other. In this letter, we show that a recent variability model can also estimate the abundances of nonlinear mixtures to some extent. We make the theoretical connection between nonlinear models and this variability model, and confirm it with experiments on nonlinearly generated synthetic datasets.