论文标题
多模式张量列车分解与空间光谱正则化，用于遥感图像恢复
Multi-mode Tensor Train Factorization with Spatial-spectral Regularization for Remote Sensing Images Recovery
论文作者
论文摘要
近年来，张量列（TT）分解和相应的TT等级可以很好地表达高级张量的低级别和模式相关性，近年来引起了很多关注。但是，基于TT分解的方法通常不足以表征沿每种三阶张量模式的低级别。受此启发的启发，我们将张量列车分解概括为模式-K张量列车分解，并引入相应的多模式张量列车（MTT）等级。然后，我们提出了一种新型的低MTT量张量完成模型，该模型通过多模式TT分解和空间光谱平滑度正则化。为了解决所提出的模型，我们开发了一种有效的近端交替最小化（PAM）算法。视觉数据的广泛数值实验结果表明，所提出的MTTD3R方法优于视觉和定量测量方面的方法。
Tensor train (TT) factorization and corresponding TT rank, which can well express the low-rankness and mode correlations of higher-order tensors, have attracted much attention in recent years. However, TT factorization based methods are generally not sufficient to characterize low-rankness along each mode of third-order tensor. Inspired by this, we generalize the tensor train factorization to the mode-k tensor train factorization and introduce a corresponding multi-mode tensor train (MTT) rank. Then, we proposed a novel low-MTT-rank tensor completion model via multi-mode TT factorization and spatial-spectral smoothness regularization. To tackle the proposed model, we develop an efficient proximal alternating minimization (PAM) algorithm. Extensive numerical experiment results on visual data demonstrate that the proposed MTTD3R method outperforms compared methods in terms of visual and quantitative measures.
