摘要
基于谱域变换的图上信号处理是网络化数据处理中的新兴理论.许多图上信号处理应用中假设图上信号的频谱以低频成分为主,而实际上图的边权重对于图上信号的频谱分布有重要影响,因此本文研究图的构造过程中的边权重设计问题.首先将其转化为最优化问题,并得到了最优边权重的解析式.进一步针对网络化数据处理中分布式计算的需求,提出了基于网络数据的分布式权重优化算法.仿真结果表明相比于传统的边权重构造方法,本文提出的算法能够使信号的能量更多地集中在图谱的低频部分.
Graph signal processing focusing on spectral analysis is an emerging theory for in-network data processing and other applications. When transforming graph signals into the spectral domain, the edge weights of graphs play an important role. Here, we formulate the design of edge weights into an optimization problem, and obtain the closed-form expression of optimal weights. We further propose the distributed optimal weighting （DOW） algorithm, which allows nodes to calculate the optimal weights in-network. Simulation results show that, compared with conventional weight design methods, the DOW algorithm enable more energy of graph signals to be aggregated upon lower frequencies.
出处
《复旦学报（自然科学版）》
CAS
CSCD
北大核心
2015年第6期679-687,共9页
Journal of Fudan University：Natural Science
基金
国家科技重大专项(2015ZX03001040)
关键词
图上信号处理
网络化数据处理
分布式最优化
拉普拉斯矩阵
graph signal processing
in-network data processing
distributed optimization
Laplacian matrix
