Spatial Low-Rank Tensor Factorization and Unmixing of Hyperspectral Images

This work presents a method for hyperspectral image unmixing based on non-negative tensor factorization. While traditional approaches may process spectral information without regard for spatial structures in the dataset, tensor factorization preserves the spectral-spatial relationship which we intend to exploit. We used a rank-(L, L, 1) decomposition which approximates the original tensor as a sum of R components. Each component is a tensor resulting from the multiplication of a low-rank spatial representation and a spectral vector. Our approach uses the spatial factors, to identify high abundance areas where pure pixels (endmembers) may lie. Unmixing is done by applying Fully Constrained Least Squares such that abundance maps are produced for each inferred endmember. Results of this method are compared against other approaches based on non-negative matrix and tensor factorizations. We observed a significant reduction of spectral angle distance for extracted endmembers and equal or better RMSE for abundance maps as compared with existing benchmarks.