A spectral mixture process conditioned by Gibbs-based partitioning

An enhanced method of spectral mixture analysis is investigated for hyperspectral imagery of moderate-to-high scene complexity, where either a large set of fundamental materials may exist throughout, or where some of the fundamental members have spectra that are similar to each other. For a complex scene, the use of one large set of fundamental materials as the set of "endmembers" for performing spectral unmixing can cause unreliable estimates of material compositions at sites within the scene. In such cases, partitioning this large set of endmembers into a number of smaller sets is appropriate, where the smaller sets are associated with certain regions in a scene. Herein, a Gibbs-based algorithm is developed to partition hyperspectral imagery into regions of similarity. This partitioning algorithm provides an estimator of an underlying and unobserved process called a "partition process" that coexists with other underlying (and unobserved) processes, one of which is called a "spectral mixing process." The algorithm exploits the properties of a Markov random field (MRF) and the associated Gibbs equivalence theorem, using a suitably defined graph structure and a Gibbs distribution to model the partition process. Consequently, spatial consistency is imposed on the spectral content of sites in each partition. The enhanced spectral mixing process is then computed as a linear mixture model that is conditioned on the partition process. Experiments are performed using scenes of HYDICE imagery to validate the algorithm, where spectral mixture analysis is performed with and without conditioning on the partitioning process.