Hyperspectral unmixing with Sparse Group Lasso

Sparse unmixing has been recently introduced as a mecha-nism to characterize mixed pixels in remotely sensed hyper-spectral images. It assumes that the observed image signa-tures can be expressed in the form of linear combinations of a number of pure spectral signatures known in advance (e.g., spectra collected on the ground by a field spectroradiometer). Unmixing then amounts to finding the optimal subset of sig-natures in a (potentially very large) spectral library that can best model each mixed pixel in the scene. In available spec-tral libraries, it is observed that the spectral signatures appear organized in groups (e.g. different alterations of a single min-eral in the U.S. Geological Survey spectral library). In this paper, we explore the potential of the sparse group lasso tech-nique in solving hyperspectral unmixing problems. Our intro-spection in this work is that, when the spectral signatures ap-pear in groups, this technique has the potential to yield better results than the standard sparse regression approach. Experi-mental results with both synthetic and real hyperspectral data are given to investigate this issue. 1