提出一种可灵活指定采样顶点的图信号采样方法，支持强制包含或排除特定节点。
Sampling Method for Generalized Graph Signals with Pre-selected Vertices via DC Optimization
- 通过DC优化设计采样算子，融合核范数与顶点选择惩罚项。
- 在真实数据和多种图信号模型上，恢复精度优于现有方法。
- 适合需要精确控制采样位置的图信号处理任务。
本文提出一种针对广义图信号的顶点级灵活采样方法，旨在基于广义采样理论实现最优恢复。该方法通过求解一个固有非凸的优化问题来设计采样算子，因最优恢复需满足秩约束。现有顶点级灵活采样方法虽能控制活跃顶点数量，但无法融入强制或禁止采样的先验知识。为此，我们构建了同时考虑活跃顶点数限制及特定顶点必须包含或排除的约束优化问题。通过核范数与差分凸（DC）惩罚项，将该问题转化为差分凸优化形式，并开发基于通用双近端梯度算法的收敛求解器。实验在多种图信号模型（包括真实数据）上验证了方法的有效性，相较于现有方法，在恢复精度方面表现更优。
原文摘要 · Abstract (English)
This paper proposes a method for vertex-wise flexible sampling of a broad class of graph signals, designed to attain the best possible recovery based on the generalized sampling theory. This is achieved by designing a sampling operator by an optimization problem, which is inherently non-convex, as the best possible recovery imposes a rank constraint. An existing method for vertex-wise flexible sampling is able to control the number of active vertices but cannot incorporate prior knowledge of mandatory or forbidden vertices. To address these challenges, we formulate the operator design as a problem that handles a constraint of the number of active vertices and prior knowledge on specific vertices for sampling, mandatory inclusion or exclusion. We transformed this constrained problem into a difference-of-convex (DC) optimization problem by using the nuclear norm and a DC penalty for vertex selection. To solve this, we develop a convergent solver based on the general double-proximal gradient DC algorithm. The effectiveness of our method is demonstrated through experiments on various graph signal models, including real-world data, showing superior performance in the recovery accuracy by comparing to existing methods.
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