A Multiobjective Group Sparse Hyperspectral Unmixing Method With High Correlation Library

Yanyi Wei, Xia Xu, Bin Pan, Tao Li, Zhenwei Shi

Abstract: Hyperspectral sparse unmixing aims at modeling pixels of hyperspectral image as a linear combination of a subset of a prior spectral library. Over the past years, spectral library has been constantly expanded, including spectra of the same material with intrinsic variability, which may result in the problem of high correlation. Recently, multiobjective sparse unmixing methods presented promising performance in dealing with sparsity via a nonconvex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathcal {L}_{0}$</tex-math></inline-formula> norm but are insensitive to identifying endmembers with high correlation. In this article, we propose a multiobjective sparse unmixing method, multiobjective group sparse hyperspectral unmixing (MO-GSU), which integrates a group sparsity structure to address high correlation of the spectral library induced by spectral variability. In order to describe the sparsity within and among groups, MO-GSU develops a mixed norm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathcal {L}_{0,q}$</tex-math></inline-formula> instead of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ \mathcal {L}_{0}$</tex-math></inline-formula> norm. During the optimization, we propose two new search strategies: intragroup local search and group-oriented adaptive genetic operator. The intragroup local search strategy is presented in addition to the multiobjective evolutionary algorithm for better exploitation within groups. The group-oriented adaptive genetic operator is designed to maintain the intergroup distribution between generations and further ensure the intragroup exploitation. Moreover, we provide theoretical proof for the advantage of the group operators in exploiting the endmembers within group. To verify the efficiency of the proposed method on high correlation situations, MO-GSU is compared with recently proposed endmember bundle based and multiobjective-based sparse unmixing methods on synthetic and real data with high correlation libraries.