Linear Spatial Spectral Mixture Model

Spectral unmixing is the process of decomposing the measured spectrum of a mixed pixel into a set of pure spectral signatures called endmembers and their corresponding abundances, which indicate the fractional area coverage of each endmember present in the pixel. A substantial number of spectral unmixing studies rely on a spectral mixture model which assumes that spectral mixing only occurs within the extent of a pixel. However, due to adjacency effect, the spectral measurement of the pixel may be contaminated by radiance from materials in neighboring pixels. In this paper, a linear spatial spectral mixture model that incorporates an adjacency effect in abundance estimation is proposed. We extend the classic linear mixture model by including a spatial term that expresses for each pixel the spectral contributions from its nearby pixels. An iterative optimization algorithm is developed to estimate fractional abundances of endmembers and a coefficient representing the overall intensity of the adjacency effect in the image. Our experimental results, with both synthetic and real hyperspectral images, demonstrate the effectiveness of the proposed model.