Manifold Based Nonlocal Second-order Regularization for Hyperspectral Image Inpainting

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.