This article studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs. Furthermore, we present an ADMM-based algorithm to solve the proposed method and establish its convergence. Numerical experiments are conducted on both synthetic and real-world data for denoising, support recovery, event detection, and semi-supervised classification.

中文翻译：

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具有非凸罚分的向量值图趋势过滤

本文研究了分段平滑图信号的去噪，这些信号在图上表现出不均匀的平滑度，其中每个节点的值都可以是矢量值。我们将图趋势过滤框架扩展为使用一系列非凸正则化器对矢量值图信号进行降噪，这些非凸正则化器的性能优于现有凸正则化器。使用oracle不等式，我们为通用图建立了所提出的非凸方法的一阶平稳点的统计误差率。此外，我们提出了一种基于ADMM的算法来解决该方法并建立其收敛性。对合成和真实数据进行了数值实验，以进行降噪，支持恢复，事件检测和半监督分类。