The fusion of hyperspectral (HS) and multispectral (MS) images designed to obtain high-resolution HS (HRHS) images is a very challenging work. A series of solutions have been proposed in recent years. However, the similarity structure of HS image has not been fully utilized. In this paper, we present a novel HS and MS image fusion method based on nonlocal low-rank tensor approximation and sparse representation. Specifically, the HS image and MS image are considered to be the spatially and spectrally degraded versions of the HRHS image respectively. Then, the nonlocal low-rank constraint term is adopted in order to form the nonlocal similarity and the spatial-spectral correlation. Meanwhile, we add the sparse constraint term to describe the sparsity of abundance. Thus, the proposed fusion model is established and its optimization is solved by alternative direction method of multipliers (ADMM). The experimental results on three synthetic data sets and one real data set show the advantages of the proposed method over several state-of-the-art competitors.

中文翻译：

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通过非局部低秩张量近似和稀疏表示的高光谱和多光谱图像融合

旨在获得高分辨率 HS (HRHS) 图像的高光谱 (HS) 和多光谱 (MS) 图像的融合是一项非常具有挑战性的工作。近年来提出了一系列解决方案。然而，HS图像的相似性结构还没有被充分利用。在本文中，我们提出了一种基于非局部低秩张量近似和稀疏表示的新型 HS 和 MS 图像融合方法。具体来说，HS 图像和 MS 图像分别被认为是 HRHS 图像的空间和光谱退化版本。然后，采用非局部低秩约束项来形成非局部相似性和空间谱相关性。同时，我们添加了稀疏约束项来描述丰度的稀疏性。因此，建立了所提出的融合模型，并通过乘法器交替方向法（ADMM）对其进行了优化。在三个合成数据集和一个真实数据集上的实验结果显示了所提出的方法相对于几个最先进的竞争对手的优势。