Learning Discriminative Sparse Representations for Modeling, Source Separation, and Mapping of Hyperspectral Imagery

A method is presented for subpixel modeling, mapping, and classification in hyperspectral imagery using learned block-structured 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 source representation and selection, thus accounting for spectral variability, small-magnitude errors, and noise. A spatial-spectral coherence regularizer in the optimization allows pixel 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 undersampled 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.