利用稀疏自表达实现高光谱影像波段选择

提出一种稀疏自表达方法来研究高光谱影像分类中的波段选择问题。该方法利用字典矩阵等于测量矩阵的条件来改进多观测向量的稀疏表达模型，将波段子集看作高光谱影像波段集合中的代表子集。稀疏自表达方法将波段选择转换为寻求多观测向量中稀疏系数矩阵的非零行向量问题，通过引入混合范数来限定非零元素行向量的个数，利用快速交替方向乘子方法求解稀疏系数矩阵，并聚类非零行向量，实现波段的有效选择。基于两个公开高光谱影像数据集并对比其他4种波段选取方法来验稀疏自表达方法。实验结果证明，稀疏自表达方法能够在计算效率明显优于基于波段相关性的线性限制最小方差方法的同时，取得与该方法和非负稀疏矩阵分解方法相匹甚至略高的总体分类精度。

Band Selection Using Sparse Self-representation for Hyperspectral Imagery

Hyperspectral imaging could collect spectrum information of ground objects on the earth surface using hundreds of bands and are widely used in recognizing subtle differences among difference ground objects. Unfortunately, numerous bands with strong intra-band correlations cause unbearable computational burdens in hyperspectral processing, and especially that seriously hinders the classification of Hyperspectral imagery (HSI) in many realistic applications. Therefore, a sparse self-representation (SSR) method was proposed to select proper bands and make dimensionality reduction on HSI data to benefit its further classification procedure. The SSR improves the sparse representation model of multiple measurement vectors (MMV) using the idea that the dictionary matrix is equal to the measurement matrix, and it regards the aimed band subset as the representative from all bands of the HSI dataset. The method formulates the band selection into finding nonzero row vectors of sparse coefficient matrix in MMV, and adopts the mixed norm to constrain the number of nonzero row vectors. The sparse coefficient matrix is solved by using fast alternating direction method of multipliers and nonzero row vectors are clustered to make proper selection from all bands. Two open HSI datasets including Urban and Pavia University are implemented to testify our SSR method and the results are compared with the other four alternative band selection methods. Experimental results show that the SSR achieves comparable even better overall classification accuracies than the linear constrained minimum variance-based band correlation constraint (LCMV-BCC) algorithm and the sparse nonnegative matrix factorization (SNMF) algorithm, whereas the computational speed of SSR significantly outperforms that of LCMV-BCC. The proposed SSR could accordingly be a good alternative to help choose proper bands from hyperspectral images.