Simultaneously Multiobjective Sparse Unmixing and Library Pruning for Hyperspectral Imagery

Abstract

Sparse hyperspectral unmixing has attracted increasing investigations during the past decade. Recent research has indicated that library pruning algorithms can significantly improve the unmixing accuracies by reducing the mutual coherence of the spectral library. Inspired by the good performance of library pruning, in this article we propose a new hyperspectral unmixing algorithm which integrates the idea of library pruning and sparse representation. An obvious challenge for pruning algorithms is that the real endmembers must be preserved after pruning. Unfortunately, recent proposed pruning algorithms, such as multiple signal classification are actually prepruning strategies, which cannot guarantee that the endmembers exactly exist in the selected spectral subset when the image noise is strong. To overcome this difficulty, we develop a simultaneous optimization approach which involves the pruning operation into the optimization process. Compared with existing prepruning-based unmixing methods, the proposed algorithm can gradually compress the search space of sparse representation, which may relieve the loss of spectral information caused by the rapid compression of the library. Instead of simply designing a regularizer, in this article we utilize a multiobjective-based framework where reconstruction error, sparsity error, and the pruning projection function are considered as three parallel objectives, so as to avoid the manually settings of regularization parameters. Moreover, we have provided theoretical analysis and proof for the reasonability of our pruning objective. Experiments on synthetic hyperspectral data may indicate the superiority of the proposed method under high-noise conditions.