为了实现高光谱图像的有效压缩采样与重构, 对分布式压缩采样的高光谱数据应用线性混合模型进行重构。首先, 在图像采集阶段, 针对高光谱图像的空谱特性, 应用分布式压缩采样策略对高光谱数据进行采集；在数据重构阶段, 应用高光谱图像的线性混合模型假设, 先对压缩数据进行端元数目的估计, 再利用估计的端元数来估计丰度矩阵, 根据端元特征信号的稀疏性质提取端元矩阵, 从而重构出原始的高光谱数据, 抛弃了压缩感知重构算法中高计算复杂性的欠定问题求解。实验结果表明：在压缩采样数据为总数据的 20%时, 重构的平均信噪比比压缩投影主成分分析算法提高了 15 dB以上, 同时该方法还便于获得端元和丰度信息。所设计的压缩感知方案采样方式简单, 重构速度快、精度高, 可应用于星载或机载的高光谱压缩感知成像。

To realize efficient compressive sampling and reconstruction, linear mixing models are used to reconstruct hyperspectral data collected by distributed compressive sampling. First, during image acquisition, distributed compressive sampling is performed to collect the hyperspectral data based on spatial and spectral characteristics of the hyperspectral image. During data reconstruction, compressive sensing reconstruction algorithms with high computational complexity for the underdetermined problem are not considered and are replaced with the original hyperspectral image reconstruction technique using the estimated endmember number, abundance, and endmember signatures based on linear mixing model assumptions. Endmember number is first calculated from the compressed data, and subsequently, abundance matrix is estimated based on the calculated endmember number. Finally, the endmember matrix is extracted depend on its sparsity. Experimental results show that the average signal noise rate after reconstruction is improved over 15 dB than compressive-projection principal component analysis algorithm. Additionally, the proposed method can conveniently obtain the endmember and abundance matrix information. The designed compressive sensing method is simple, fast and accurate and can be applied to compressive sensing hyperspectral imaging utilizing spaceborne or airborne sensors.