In this article, we address the super-resolution problems, which estimate the high-resolution multispectral images from the multispectral Sentinel-2 (S2) images with different resolutions. Since S2 images can be naturally represented by tensors, we reformulate the degradation process as the tensor-based form. Based on the degradation mechanism, we build a tensor-based optimization model for S2 images super-resolution problem, which fully exploits intrinsic nonlocal spatial similarity and global spectral redundancy. Specifically, the model consists of the data fidelity term and the low-multirank regularizer tailored to thoroughly mining the inherent spatial-nonlocal and spectral redundancy. Then, we develop an efficient alternating direction method of multipliers algorithm with theoretically guaranteed convergence to tackle the resulting tensor optimization problem. Numerical experiments including simulated and real data demonstrate that our method outperforms the competing methods visually and qualitatively.

中文翻译：

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NSTMR：使用张量多秩的非局部非凸代理的 Sentinel-2 图像的超分辨率

在本文中，我们解决了超分辨率问题，即从具有不同分辨率的多光谱 Sentinel-2 (S2) 图像中估计高分辨率多光谱图像。由于 S2 图像可以自然地由张量表示，我们将退化过程重新表述为基于张量的形式。基于退化机制，我们为 S2 图像超分辨率问题构建了一个基于张量的优化模型，该模型充分利用了内在的非局部空间相似性和全局光谱冗余。具体来说，该模型由数据保真度项和低多秩正则化器组成，用于彻底挖掘固有的空间非局部和光谱冗余。然后，我们开发了一种有效的乘法器交替方向方法，理论上保证收敛，以解决由此产生的张量优化问题。包括模拟和真实数据在内的数值实验表明，我们的方法在视觉上和定性上都优于竞争方法。