Hypergraph Learning and Reweighted $\\ell _1$-Norm Minimization for Hyperspectral Unmixing

Abstract

Hyperspectral image unmixing techniques are developing to tackle the problem of mixed pixels caused by low spatial resolutions. In sparse unmixing, the redundant spectral library of materials is provided beforehand as <italic>a priori</italic> information to find the optimal representation by sparse linear regression. In order to improve the estimation of abundance distributions, the spatial correlation is taken into account and hypergraph learning is introduced to make full use of the underlying spatial-contextual information. Specifically, we find <inline-formula><tex-math notation= LaTeX >$K$</tex-math></inline-formula>-nearest pixels of each pixel in spectral domains from a local region and construct a hypergraph to exploit the fact that spatial neighboring pixels have a high probability of sharing similar spectral information. Furthermore, a reweighted <inline-formula><tex-math notation= LaTeX >$\\ell _1$</tex-math></inline-formula>-norm minimization scheme is adopted instead to enhance the sparsity of estimated fractional abundances. The complicated large-scale regression problem is decomposed into subproblems to obtain the optimal solution within the framework of alternating direction method of multipliers. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of the proposed algorithm.