基于扩散算子的带限图信号加权重建策略

Graph Diffusion Operator Based Weighted Reconstruction Strategy for Band-limited Graph Signals

图信号处理技术将经典信号处理的概念和算法延展到图结构信号的处理领域。对于带限图信号,可以通过分析信号之间的关联性,重建出未采样的信号。该文分析了未采样信号的构成架构,提出一个基于扩散算子的未采样信号迭代重建算法。在每次迭代过程中,将已采样信号的重建残差扩散至所有未采样的信号节点,并进一步通过初步估计结果与重建残差的加权处理,提升算法的收敛速度。采用合成数据和真实数据进行仿真验证,实验结果显示所提出的算法具有低重建误差和快速收敛的特点。

Signal processing on graphs extends signal processing concepts and methodologies from the classical signal processing theory to data indexed by general graphs. For a band-limited graph signal, the unsampled data can be reconstructed from the sampled data by exploiting the relationship of the graph signals. This paper proposes a concept of graph diffusion operator for signal processing on graphs, and uses the operator to reconstruct band-limited graph signals from the sampled data. In each iteration, the residuals of the sampled vertices are propagated to all the unsampled vertices, and the known information and initial estimated results are further exploited via weighted process, aiming at accelerating the convergence. An analysis framework is proposed for the unsampled graph signals. The simulation results of synthetic data and real-world data demonstrate the wonderful effectiveness of the proposed reconstruction strategy.