Sparsity measure based library aided unmixing of hyperspectral image

Availability of a large number of application-specific spectral libraries has generated a great deal of interest in semi-blind unmixing of the hyperspectral image in both remote sensing and signal processing community. This study presents a novel, semi-supervised, parameter-free algorithm which employs sparsity measures for library pruning. The overall algorithm includes sparsity criteria based library pruning and sparse inversion method for abundance computation. In the pruning process, each library element is removed from the spectral library and the corresponding sparse abundance matrix is computed. The library elements which lead to higher sparsity are adjudged as image endmembers, based on the assumption that elimination of actual image endmember enhances sparsity level. The authors also present a detailed exploration of standard sparsity measures. They calculate the abundance of the pruned library by maximising Gini index or pq-norm sparsity, which satisfies the desirable sparsity properties and is easier to compute. The abundance calculation task is solved using the adaptive direction method of multipliers. The experimental results on several real and synthetic image datasets demonstrate the computational efficiency and proficiency the authors' method in the presence of noise and highly coherent spectral library.