Sparsity Constrained Graph Regularized NMF for Spectral Unmixing of Hyperspectral Data

Hyperspectral images contain mixed pixels due to low spatial resolution of hyperspectral sensors. Mixed pixels are pixels containing more than one distinct material called endmembers. The presence percentages of endmembers in mixed pixels are called abundance fractions. Spectral unmixing problem refers to decomposing these pixels into a set of endmembers and abundance fractions. Due to nonnegativity constraint on abundance fractions, nonnegative matrix factorization methods (NMF) have been widely used for solving spectral unmixing problem. In this paper we have used graph regularized NMF (GNMF) method combined with sparseness constraint to decompose mixed pixels in hyperspectral imagery. This method preserves the geometrical structure of data while representing it in low dimensional space. Adaptive regularization parameter based on temperature schedule in simulated annealing method also has been used in this paper for the sparseness term. Proposed algorithm is applied on synthetic and real datasets. Synthetic data is generated based on endmembers from USGS spectral library. AVIRIS Cuprite dataset is used as real dataset for evaluation of proposed method. Results are quantified based on spectral angle distance (SAD) and abundance angle distance (AAD) measures. Results in comparison with other methods show that the proposed method can unmix data more effectively. Specifically for the Cuprite dataset, performance of the proposed method is approximately 10% better than the VCA and Sparse NMF in terms of root mean square of SAD.