Hyperspectral image unmixing involving spatial information by extending the alternating least-squares algorithm

Hyperspectral images, in contrast to common RGB images, offer the possibility to not only determine the pure materials present in a scene, but also material abundances in mixtures. The calculation of the material fractions with the so-called linear mixing model is not unique, an infinite number of solutions exists. Therefore, additional constraints should be incorporated. Some algorithms involve spatial constraints explicitly, e. g., they assume that the abundances mostly do not change considerably from one pixel to another. Recently, we presented such algorithms. The calculation time with spatial constraints included, however, is rather long, so it was checked if there is a faster way to include the spatial information. In this paper, we extend the well-known alternating least-squares algorithm to implicitly include the previously used spatial information in a slightly different way, namely by adding an extra image denoising step to the calculation. The extended algorithm is called ALSmooth. We compare the computing time and the results of the ALSmooth and the previously presented algorithms. For this purpose, laboratory data of mixtures with known ground truth had been acquired. Both the previously investigated algorithms and the ALSmooth algorithm are quite sensitive towards parameter value changes; the ALSmooth algorithm is even more sensitive. For certain applications with defined environment and endmembers, however, it can be a faster alternative.