This paper proposes a general framework to use the cross tensor approximation or tensor ColUmn-Row (CUR) approximation for reconstructing incomplete images and videos. The key importance of the new algorithms is their simplicity and ease of implementation with low computational complexity. For the case of data tensors with 1) structural missing components or 2) a high missing rate, we propose an efficient smooth tensor CUR algorithms which first make the sampled fibers smooth and then apply the proposed CUR algorithms. The numerical experiments show the significant benefit of this smoothing procedure. The main contribution of this paper is to develop/investigate improved multistage CUR algorithms with filtering (smoothing ) preprocessing for tensor completion. The second contribution is a detailed comparison of the performance of image recovery for four different CUR strategies via extensive computer simulations. Our simulations clearly indicated that the proposed algorithms are much faster than most of the existing state-of-the-art algorithms developed for tensor completion, while performance is comparable and often even better. Furthermore, we will provide in GitHub the MATLAB codes which can be used for various applications. Moreover, to our best knowledge, the CUR (cross approximation) algorithms have not been investigated nor compared till now for image and video completion.
翻译:本文提出一个通用框架, 用于重建不完全的图像和视频。 新的算法的关键重要性在于其简单和容易实施, 且计算复杂度低。 对于数据分解(1) 结构缺失部件或2) 缺失率高的数据分解器, 我们提出一个高效的光滑高压 CUR 算法, 首先让样本纤维平滑, 然后应用拟议的 CUR 算法。 数字实验显示了这种平滑程序的巨大好处。 本文的主要贡献是开发/ 投资平台改进了具有过滤( mooothing) 预处理的多阶段 CUR 算法, 以预处理高压完成。 第二个贡献是详细比较四个不同的 CUR 战略通过广泛的计算机模拟恢复图像的性能。 我们的模拟清楚地表明, 拟议的算法比大多数为慢速完成而开发的现有状态- 艺术算法要快得多, 而性能是可比的, 并且往往更好。 此外, 我们将在GitHub中提供用于过滤( mooging) 多阶段的 CATLAB 代码, 在各种应用中, 之前, 和 Viralalalation 之前, 我们的最佳的算法已经用于了各种应用。