Abundance Estimation Using Discontinuity Preserving and Sparsity-Induced Priors

Abstract

Abundance estimation is used to infer the proportions of endmembers with the given endmember signatures and reflectance value at each location. In this paper, we propose a two-phase iterative approach to estimate the abundances (fractions) of materials (endmembers) from the pixels of hyperspectral images (HSIs) by using the energy minimization framework. A linear mixture model is used to define the data term. We observe that abundance maps have homogeneous regions with limited discontinuity, and they exhibit spatial redundancy. Hence, we use inhomogeneous Gaussian Markov random field (IGMRF) and sparsity-induced priors as the regularization terms. While the IGMRF prior captures the smoothness and preserves discontinuities among abundance values, the sparsity-induced prior accounts for redundancy. We calculate the IGMRF parameters at every pixel location and learn a dictionary and the sparse representation for abundances using the initial estimate in phase 1, while the final abundance maps are estimated in phase 2. In order to learn the sparsity, we use the approach based on K-singular value decomposition. Both the IGMRF and sparseness parameters are initialized using an initial estimate of abundances and refined using the two-phase iterative approach. The experiments are conducted on synthetic hyperspectral HSIs with different noise levels, as well as on two real HSIs. The results are qualitatively and quantitatively compared with state-of-the-art approaches. Experimental results demonstrate the effectiveness of the proposed approach.