压缩感知理论提供了一种新的数据采集思路. 基于该理论提出了一种高光谱数据采集和图像重构方法，以波段分组的方式将高光谱各波段分为参考波段和普通波段，对各波段图像单独采用分块压缩感知测量以获取高光谱数据. 在图像重构过程中，参考波段采用平滑投影Landweber算法重构. 对于普通波段，结合谱间预测和平滑投影Landweber提出了一种新算法: 先采用谱间双向预测得到预测图像，然后对预测图像进行分块压缩感知测量获得测量值，并计算它与该波段原测量值之间的差值，再由测量差值重构预测差值来迭代恢复原波段图像. 该方法在数据重构过程中充分考虑了高光谱图像的谱间相关性和空间相关性，能提高图像重构精度. 实验结果表明，利用所提出的方法重构高光谱图像，其性能优于多向量压缩感知方法和分块压缩感知测量后直接对各波段图像单独重构的方法.
Compressed sensing (CS) provides a new method for data acquisition. Ahyperspectral images CS
methodology is proposed in this paper. In the proposed framework, hyperspectral images are divided into
several groups, and each group consists of a reference band followed by some common bands. Random measurements of the individual spectral bands are obtained using block CS independently. In image reconstruction,the reference bands are reconstructed with the smoothed projected Landweber algorithm, and the common bands with a new reconstruction algorithm. The algorithm is implemented as follows: 1) Obtain predicted values of the common bands using the spectral bidirectional prediction. 2) Calculate measurement differences using block observation on the predicted values. 3) Reconstruct the images and their corresponding prediction differences in an iterative fashion. This method can improve reconstruction quality as it has fully considered the spectral and spatial correlations. Experimental results reveal that reconstruction performance of the proposed method is substantially superior to that by applying 2-D image reconstruction independently and that of a multiple-vector CS variant method.
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