In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor completion methods using TT decomposition have two obvious drawbacks. One is that they only consider mode weights according to the degree of mode balance, even though some elements are recovered better in an unbalanced mode. The other is that serious blocking artifacts appear when the missing element rate is relatively large. To remedy such two issues, in this work, we propose a novel tensor completion approach via the element-wise weighted technique. Accordingly, a novel formulation for tensor completion and an efficient optimization algorithm, called as tensor completion by parallel weighted matrix factorization via tensor train (TWMac-TT), is proposed. In addition, we specifically consider the recovery quality of edge elements from adjacent blocks. Different from traditional reshaping and ket augmentation, we utilize a new tensor augmentation technique called overlapping ket augmentation, which can further avoid blocking artifacts. We then conduct extensive performance evaluations on synthetic data and several real image data sets. Our experimental results demonstrate that the proposed algorithm TWMac-TT outperforms several other competing tensor completion methods.
翻译:近年来,基于高压列车(TT)格式,基于高压列车(TT)格式的先进完成应用数量不断增加,原因是其在处理高阶高压数据方面的效率和有效性。然而,使用TT分解法的现有先进完成方法有两个明显的缺点。其中之一是,它们只考虑模式平衡程度的模式权重,尽管有些元素在不平衡模式中恢复得更好。另一个是,当缺失元素率相对较大时,严重阻塞工艺就会出现。在这项工作中,为了通过元素加权技术纠正这两个问题,我们建议采用新颖的散装完成法。因此,我们提出了一种用于高压完成和高效优化算法的新配方,即通过高压列列车(TWMac-TT)平行加权矩阵因子化而完成。此外,我们特别考虑邻近地区边缘元素的回收质量。不同于传统的重塑和增强元件率,我们使用一种称作重叠增殖的新型变压技术,可以进一步避免阻断产。我们随后对合成数据和若干真实图像数据集进行广泛的绩效评估。我们的一些实验结果显示,我们的拟议演算方法是TW的。