压缩感知重建是解决高光谱现有成像模式数据量大冗余度高问题的一个有效机制。针对高光谱图像的多通道特性，该文建立了高光谱压缩感知的多测量向量模型，编码端使用随机卷积算子对各通道进行快速采样，生成测量向量矩阵。解码端构建图稀疏正则化的联合重建模型，在稀疏变换域将高光谱图像分解为谱间的关联成分和差异成分，通过图结构化稀疏度量表征关联成分的空谱相关性，并约束谱间差异成分的稀疏性。进一步提出模型求解的交替方向乘子迭代算法，通过引入辅助变量与线性化技巧，使得每一子问题均存在解析解，降低了模型求解的复杂度。对多个实测数据集进行了对比实验，实验结果验证了该文模型与算法的有效性。%Compressed Sensing (CS) reconstruction of hyperspectral image is an effective mechanism to comedy the traditional hyperspectral imaging pattern with the drawback of high redundancy and vast data volume. This paper presents a new multiple measurement vector model for compressed sensing reconstruction of hyperspectral data in consideration of its multiple channel character. In the encoding side, the random convolution operator is used to rapidly obtain the measurement vector of each channel which is subsequently reorganized as a measurement vector matrix. In the decoding side, a joint reconstruction model is proposed to reconstruct the hyperspectral data from the multiple measurement vectors. The model decomposes the hyperspectral data into the inter-channel correlated and differenced component in the sparsifying transform domain, where the correlated component with high spatial and spectral correlation is constrained to be graph structured sparse and the differenced component is constrained to be l1 sparse. A numerical optimization algorithm is also proposed to solve the reconstruction model by the alternating direction method of multiplier. Every sub-problem in the iteration formula admits analysis solution by introducing the auxiliary variable and linearization operation. The complexity of the numerical optimization algorithm is reduced. The experimental results demonstrate the effectiveness of the proposed algorithm.
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