发表机构
The University of Osaka; Tokyo University of Agriculture and Technology（大阪大学; 东京农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于深度算法展开（DAU）的时变图信号恢复方法，结合时空正则项展开迭代共轭梯度法，在多数据集实验中验证了所提方法的有效性。
AI 中文摘要
本文提出一种基于深度算法展开（DAU）的时变图信号恢复方法。时变图信号（如传感器网络获取的信号）在空间上非均匀分布，表现为时间序列，这类观测信号常含噪声与缺失值，其恢复需同时考虑空间与时间关系。所提方法基于优化问题，该问题通过时空正则项建模信号特性，正则项结合用于空间平滑的Sobolev算子与用于时间平滑的多抽头有限脉冲响应（FIR）滤波器；随后将迭代共轭梯度法展开以求解该问题，并在各迭代中学习正则化参数与滤波器系数。该方法可应用于监督批量、监督在线及无监督批量设置以学习上述参数。在多个合成与真实数据集上的实验表明，监督批量方法在几乎所有场景中均取得最低均方根误差（RMSE）；监督在线与无监督批量方法优于各自设置下的现有方法，且常与现有批量方法具有竞争力。
英文摘要
In this paper, we propose restoration methods for time-varying graph signals using deep algorithm unrolling (DAU). Time-varying graph signals, such as signals obtained from sensor networks, are nonuniformly distributed in space and observed as time series. Since these observed signals often contain noise and missing values, their restoration needs to consider both spatial and temporal relationships. Our approach is based on an optimization problem that models signal properties using a spatiotemporal regularizer that combines a Sobolev operator for spatial smoothness and a multi-tap FIR filter for temporal smoothness. We then unroll the iterative conjugate gradient method to solve this problem and learn the regularization parameters and filter coefficients in each iteration. Our method can be applied to supervised batch, supervised online, and unsupervised batch settings to learn these parameters. Experiments on several synthetic and real-world datasets show that the supervised batch method achieves the lowest RMSEs in almost all cases. The supervised online and the unsupervised batch methods outperform the existing methods of their own settings, and are often competitive with the existing batch methods.
CommentsSubmitted to IEEE Transactions on Signal and Information Processing over Networks
