A Multiobjective Cooperative Coevolutionary Algorithm for Hyperspectral Sparse Unmixing

Abstract

Sparse unmixing of hyperspectral data is an important technique aiming at estimating the fractional abundances of the endmembers. Traditional sparse unmixing is faced with the $\boldsymbol {l_{0}}$ -norm problem which is an NP-hard problem. Sparse unmixing is inherently a multiobjective optimization problem. Most of the recent works combine cost functions into single one to construct an aggregate objective function, which involves weighted parameters that are sensitive to different data sets and difficult to tune. In this paper, a novel multiobjective cooperative coevolutionary algorithm is proposed to optimize the reconstruction term, the sparsity term and the total variation regularization term simultaneously. A problem-dependent cooperative coevolutionary strategy is designed because sparse unmixing encounters a large scale optimization problem. The proposed approach optimizes the nonconvex $\boldsymbol {l_{0}}$ -norm problem directly and can find a better compromise between two or more competing cost function terms automatically. Experimental results on simulated and real hyperspectral data sets demonstrate the effectiveness of the proposed method.