Completing a data tensor with structured missing components is a challenging task where the missing components are not distributed randomly but they admit some regular patterns, e.g. missing columns and rows or missing blocks/patches. Many of the existing tensor completion algorithms are not able to handle such scenarios. In this paper, we propose a novel and efficient approach for matrix/tensor completion by applying Hankelization and distributed tensor ring decomposition. Our main idea is first Hankelizing an incomplete data tensor in order to obtain high-order tensors and then completing the data tensor by imposing sparse representation on the core tensors in tensor ring format. We apply an efficient over-complete discrete cosine transform dictionary and sparse representation techniques to learn core tensors. Alternating direction methods of multiplier and accelerated proximal gradient approaches are used to solve the underlying optimization problems. Extensive simulations performed on image, video completions and time series forecasting show the validity and applicability of the method for different kinds of structured and random missing elements.

用结构化的缺失组件完成数据张量是一项具有挑战性的任务，其中缺失的组件不是随机分布的，但它们承认一些规则模式，例如缺失的列和行或缺失的块/补丁。许多现有的张量补全算法无法处理此类场景。在本文中，我们通过应用 Hankelization 和分布式张量环分解提出了一种新颖有效的矩阵/张量补全方法。我们的主要思想是首先对一个不完整的数据张量进行汉克化以获得高阶张量，然后通过对核心张量以张量环格式进行稀疏表示来完成数据张量。我们应用高效的过完备离散余弦变换字典和稀疏表示技术来学习核心张量。乘法器和加速近端梯度方法的交替方向方法用于解决潜在的优化问题。对图像、视频补全和时间序列预测进行的大量模拟显示了该方法对不同类型的结构化和随机缺失元素的有效性和适用性。