Spatial regularization for the unmixing of hyperspectral images

For demanding sorting tasks, the acquisition and processing of color images does not provide sufficient information for the successful discrimination between the different object classes that are to be sorted. An alternative to integrating three spectral regions of visible light to the three color channels is to sample the spectrum at up to several hundred, evenly-spaced points and acquire so-called hyperspectral images. Such images provide a complete image of the scene at each considered wavelength and contain much more information about the composition of the different materials. Hyperspectral images can also be acquired in spectral regions neighboring visible light such as, e.g., the ultraviolet (UV) and near-infrared (NIR) region. From a mathematical point of view, it is possible to extract the spectra of the pure materials and the amount to which these spectra contribute to material mixtures. This process is called spectral unmixing. Spectral unmixing based on the mostly used linear mixing model is a difficult task due to model ambiguities and distorting factors such as noise. Until a few years ago, the most inherent property of hyperspectral images, that is to say, the abundance correlation between neighboring pixels, was not used in unmixing algorithms. Only recently, researchers started to incorporate spatial information into the unmixing process, which by now is known to improve the unmixing results. In this paper, we will introduce two new methods and study the effect of these two and two already described methods on spectral unmixing, especially on their ability to account for edges and other shapes in the abundance maps.