中文摘要：

提出了一种新的空间一光谱字典学习方法，用于不完备高光谱图像的重构。根据高光谱图像具有丰富的空间和谱间相关性的特点，将高光谱图像分割成三维重叠的小立方体块，从中学习出能够对这些块进行稀疏表示的空间一光谱字典。首先固定字典，用非负正交匹配追踪法计算稀疏系数；然后固定系数，用梯度下降法更新字典，上述两步交替进行直到算法收敛。依据这种分块模型学习出的字典更符合高光谱图像的特点。在谱向上字典原子为物质的光谱反射曲线，在空间向上字典为普通二维空间块字典。最后将字典应用于不完备高光谱图像的重构，实验结果表明，该方法以较低的采样率获得了良好的重构效果。

英文摘要：

A novel spatial-spectral dictionary learning algorithm is proposed and applied to reconstruct the incomplete hy- perspectral images. According to the characteristic that hyperspectral images have rich spatial and spectral correlations,the hyperspectral image is divided into 3D small overlapping cube blocks. The spatial-spectral dictionary that can represent these blocks sparsely is learned. First, assuming the dictionary is fixed, non-negative orthogonal match pursuit method is used to calculate the sparse coefficients ;second, assuming the coefficients are fixed,gradient descent method is used to up-date the dictionary ;these two steps are alternately used until the algorithm is converged. The dictionary learned from this block model is consistent with the characteristics of the hyperspectral images. At the spectral direction ,the dictionary atoms are the spectral reflection curves of the real materials;at the spatial direetion,the dictionary is ordinary 2D spatial bloek dictionary. The spatial-spectral dictionary was applied to reconstruct the incomplete hyperspectral images. Experiment results show that this algorithm can achieve satisfied results with a low sampling rate.