基于空谱联合的多假设预测高光谱图像压缩感知重构算法

为充分利用高光谱图像的空间相关性和谱间相关性，该文提出一种基于空谱联合的多假设预测压缩感知重构算法。将高光谱图像分组为参考波段图像和非参考波段图像，参考波段图像利用光滑Landweber投影算法重构，对于非参考波段图像，引入空谱联合的多假设预测模型，提高重构精度。非参考波段图像中每个图像块的预测值不仅来自非参考波段图像未经预测的初始重构值的相邻图像块，而且来自参考波段重构图像相应位置及其邻近的图像块，利用预测值得到测量域中的残差，然后对残差进行重构并对预测值进行修正，此残差比原图像更稀疏，且算法采用迭代方式提高重构图像的精度。借助Tikhonov正则化方法求解多假设预测的权重系数，并基于结构相似性判断是否改变多假设预测搜索窗口大小，最后利用交叉验证计算重构算法终止迭代的判据参数。实验结果表明，所提算法优于仅利用空间相关性或谱间相关性进行预测和不预测的重构算法，其重构图像的峰值信噪比提高2 dB以上。

Compressed Sensing Reconstruction of Hyperspectral Images Based on Spatial-spectral Multihypothesis Prediction

Compressed Sensing (CS) reconstruction of hyperspectral images driven by spatial-spectral multihypothesis prediction is proposed in order to take full advantage of spatial and spectral correlation of hyperspectral images. The hyperspectral images are grouped into reference band images and non-reference band images, and the reference band images are reconstructed by Smoothed Projected Landweber (SPL) algorithm. For the non-reference band images, the spatial-spectral multihypothesis prediction model is introduced to improve the reconstruction accuracy. Multihypothesis predictions drawn for an image block of non-reference band image are made not only from spatially surrounding image blocks within an initial non-predicted reconstruction of non-reference band image, but also from the corresponding position and neighboring image blocks within the reconstruction of reference band image. The resulting predictions are used to generate residuals in the projection domain, and the residuals are reconstructed to revise the prediction values. The residuals being typically more compressible than the original images and the iterative execution mode lead to improved reconstruction quality. Tikhonov regularization is utilized to solve the weight coefficients of multihypothesis prediction and structural similarity is used as a criterion to decide whether to change the search window size or not. Cross validation is presented to compute the criterion parameter of iteration termination. Experimental results demonstrate that the proposed algorithm outperforms alternative strategies only using spatial correlation or spectral correlation to predict or not employing prediction and the peak signal-to-noise ratio of its reconstructed images is increased by more than 2 dB.