Joint Graph and Vertex Importance Learning

On Critical Sampling of Time-Vertex Graph Signals

Joint time-vertex graph signals are pervasive in real-world. This paper focuses on the fundamental problem of sampling and reconstruction of joint time-vertex graph signals. We prove the existence and the necessary condition of a critical sampling set using minimum number of samples in time and graph domain respectively. The theory proposed in this paper suggests to assign heterogeneous sampling pattern for each node in a network under the constraint of minimum resources. An efficient algorithm is also provided to construct a critical sampling set.

面向数据驱动的图学习与采样集联合优化

Towards joint graph learning and sampling set selection from data

本文提出联合优化图结构与采样集的方法，通过顶点重要性采样（VIS）及带排斥的变体（VISR），在模拟数据上实现优于传统两步法的重建性能与更低复杂度。

Graph Vertex Sampling with Arbitrary Graph Signal Hilbert Spaces

Graph vertex sampling set selection aims at selecting a set of ver-tices of a graph such that the space of graph signals that can be reconstructed exactly from those samples alone is maximal. In this context, we propose to extend sampling set selection based on spectral proxies to arbitrary Hilbert spaces of graph signals. Enabling arbitrary inner product of graph signals allows then to better account for vertex importance on the graph for a sampling adapted to the application. We first state how the change of inner product impacts sampling set selection and reconstruction, and then apply it i…

基于不确定性原理的广义图信号重建

Generalized Graph Signal Reconstruction via the Uncertainty Principle

本文提出广义图信号的新型不确定性原理，通过联合顶点-时间与频谱-频率展宽构建能量集中原子字典，以提升不完整或间歇数据下的信号重建精度与噪声鲁棒性。

图线性调频信号与图分数阶顶点-频率能量分布

Graph Chirp Signal and Graph Fractional Vertex-Frequency Energy Distribution

该研究首次正式定义图线性调频信号，构建其分析理论框架，提出图分数阶顶点-频率能量分布及相关分布、检测方法，在噪声环境信号检测与真实数据降噪上表现更优。

JFRFFNet：一种具有部分先验信息的数据-模型协同驱动的图信号去噪模型

JFRFFNet: A Data-Model Co-Driven Graph Signal Denoising Model with Partial Prior Information

针对传统图信号去噪需完整先验信息的问题，提出数据-模型协同驱动的JFRFFNet，将JFRFT域维纳滤波嵌入神经网络，仅用部分先验信息即可去噪，显著提升输出信噪比。