Hyperspectral super-resolution is commonly accomplished by the fusing of a hyperspectral imaging of low spatial resolution with a multispectral image of high spatial resolution, and many tensor-based approaches to this task have been recently proposed. Yet, it is assumed in such tensor-based methods that the spatial-blurring operation that creates the observed hyperspectral image from the desired super-resolved image is separable into independent horizontal and vertical blurring. Recent work has argued that such separable spatial degradation is ill-equipped to model the operation of real sensors which may exhibit, for example, anisotropic blurring. To accommodate this fact, a generalized tensor formulation based on a Kronecker decomposition is proposed to handle any general spatial-degradation matrix, including those that are not separable as previously assumed. Analysis of the generalized formulation reveals conditions under which exact recovery of the desired super-resolved image is guaranteed, and a practical algorithm for such recovery, driven by a blockwise-group-sparsity regularization, is proposed. Extensive experimental results demonstrate that the proposed generalized tensor approach outperforms not only traditional matrix-based techniques but also state-of-the-art tensor-based methods; the gains with respect to the latter are especially significant in cases of anisotropic spatial blurring.

翻译：高光谱超分辨率通常通过融合低空间分辨率的高光谱图像与高空间分辨率的多光谱图像实现，近期已涌现诸多基于张量的方法。然而，此类张量方法均假设从目标超分辨率图像生成观测高光谱图像的空间模糊操作可分解为独立水平与垂直模糊。最新研究指出，此类可分离的空间退化难以模拟真实传感器（例如可能呈现各向异性模糊）的实际运作。为适应这一事实，本文提出基于克罗内克分解的广义张量公式，可处理任意一般空间退化矩阵，包括先前假设中不可分离的情形。通过对广义公式的理论分析，揭示了保证目标超分辨率图像精确重建的条件，并提出一种基于块组稀疏正则化的实用重建算法。大量实验结果表明，所提出的广义张量方法不仅优于传统基于矩阵的技术，更超越了当前最先进的张量方法；在存在各向异性空间模糊的场景中，相较于后者的性能提升尤为显著。