Learning Discriminative Sparse Models for Source Separation and Mapping of Hyperspectral Imagery

A method is presented for sub-pixel mapping and classification in hyperspectral imagery, using learned blockstructured discriminative dictionaries, where each block is adapted and optimized to represent a material in a compact and sparse manner. The spectral pixels are modeled by linear combinations of subspaces defined by the learned dictionary atoms, allowing for linear mixture analysis. This model provides flexibility in the sources representation and selection, thus accounting for spectral variability, small-magnitude errors, and noise. A spatial-spectral coherence regularizer in the optimization allows for pixels classification to be influenced by similar neighbors. We extend the proposed approach for cases for which there is no knowledge of the materials in the scene, unsupervised classification, and provide experiments and comparisons with simulated and real data. We also present results when the data have been significantly under-sampled and then reconstructed, still retaining high-performance classification, showing the potential role of compressive sensing and sparse modeling techniques in efficient acquisition/transmission missions for hyperspectral imagery. Alexey Castrodad and Guillermo Sapiro are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, 55455 USA e-mail: {castr103, guille}@umn.edu. Alexey Castrodad, John Greer, and Edward Bosch are with the Department of Defense. Zhengming Xing and Lawrence Carin are with the Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 USA e-mail:{zhengming.xing, lcarin}@duke.edu. September 27, 2010 DRAFT IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. X, NO. X, JANUARY XXXX 1 Learning Discriminative Sparse Models for Source Separation and Mapping of Hyperspectral Imagery