Integrating Spatial Information in Unsupervised Unmixing of Hyperspectral Imagery Using Multiscale Representation

This paper presents an unsupervised unmixing approach that takes advantage of multiscale representation based on nonlinear diffusion to integrate the spatial information in the spectral endmembers extraction from a hyperspectral image. The main advantages of unsupervised unmixing based on multiscale representation (UUMR) are the avoidance of matrix rank estimation to determine the number of endmembers and the use of spatial information without employing spatial kernels. Multiscale representation builds a family of smoothed images where locally spectrally uniform regions can be identified. The multiscale representation is extracted solving a nonlinear diffusion partial differential equation (PDE). Locally, homogeneous regions are identified by taking advantage of an algebraic multigrid method used to solve the PDE. Representative spectra for each region are extracted and then clustered to build spectral endmember classes. These classes represent the different spectral components of the image as well as their spectral variability. The number of spectral endmember classes is estimated using the Davies and Bouldin validity index. A quantitative assessment of unmixing approach based on multiscale representation is presented using an AVIRIS image captured over Fort. A.P. Hill, Virginia. A comparison of UUMR results with others unmixing techniques is included.