The low-dimensional manifold of image patches has been introduced as regularizer term, and shown effective in hyperspectral image inpainting. However, in this article, we find that using only the low-dimensional property of manifold may not always generate smooth results. In terms of this, we first present a higher order term to the low-dimensional manifold model, namely nonlocal second-order regularization (NSR), which provides better approximation to the real data distribution and manifests both the properties of low dimensionality and smoothness. Moreover, in order to balance the known and unknown sets, we further propose a weighted version of NSR, called WNSR. The generalized minimal residual algorithm is adopted to solve this unsymmetrical model, in which a semi-patch is applied for acceleration of the nearest neighbor search. Finally, we conduct intensive numerical experiments on five well-known datasets to verify the superiority of our method. The inpainting results show that our proposed (W)NSR significantly outperforms the state-of-the-art methods with respect to both visual and numerical quality.

中文翻译：

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用于高光谱图像修复的基于流形的非局部二阶正则化

图像块的低维流形已被引入作为正则项，并在高光谱图像修复中显示出有效。然而，在本文中，我们发现仅使用流形的低维属性可能并不总是产生平滑的结果。对此，我们首先向低维流形模型提出了一个高阶项，即非局部二阶正则化（NSR），它提供了对真实数据分布的更好的近似，同时体现了低维和平滑的特性。此外，为了平衡已知和未知集，我们进一步提出了 NSR 的加权版本，称为 WNSR。采用广义最小残差算法来解决这种不对称模型，其中应用半补丁来加速最近邻搜索。最后，我们对五个众所周知的数据集进行了密集的数值实验，以验证我们方法的优越性。修复结果表明，我们提出的 (W)NSR 在视觉和数值质量方面都明显优于最先进的方法。