The adaptive inverse scale space method for hyperspectral unmixing

This paper deals with the problem of hyperspectral unmixing. We investigate the behavior of non-negative least squares (NNLS) as well as sparse ℓ¹ unmixing and show that while the NNLS method does not take noise into account, the ℓ¹ approach is biased towards smaller abundances and lower contrast. The application of the adaptive inverse scale space method, which we originally developed for compressed sensing, yields sparse results with optimal data fidelity. Furthermore, we will show that it naturally offers a multiscale decomposition of the image into several abundance maps based on the materials importance. Our method is fast, easy to implement and has an interpretation as a refinement of the spectral angle mapper (SAM).