基于图谱域移位的带限图信号重构算法  

Graph Band-limited Signals Reconstruction Method Based Graph Spectral Domain Shifting

作　　者：杨杰[1] 赵磊[1] 郭文彬[1,2] YANG Jie;ZHAO Lei;GUO Wen-Bin(Beijing University of Posts and Telecommunications,Beijing 100786;Science and Technology on Information Transmission and Dissemination in Communication Networks Laboratory,Shijiazhuang 050000)

机构地区：[1]北京邮电大学,北京100786 [2]通信网信息传输与分发技术重点实验室,石家庄050000

出　　处：《自动化学报》2021年第9期2159-2169,共11页Acta Automatica Sinica

基　　金：国家自然科学基金(61271181)资助。

摘　　要：针对带限图信号的重构问题,本文提出了基于图谱域移位的带限图信号重构模型,该模型将图带限分量的恒等不变特性建模为最小二乘问题.基于所提出的重构模型,本文设计了基于谱移位的重构算法和基于残差谱移位的重构算法.相比于其他重构算法,两种新算法提升了迭代效率和重构精度.此外,本文算法还适用于分段带限图信号的重构问题,并且具有良好的迭代效率和重构精度.通过实验仿真表明,相比于目前其他的带限图信号重构算法,新算法的迭代效率提升约70%和重构精度提升约60%.Aiming at the problem of graph band-limited signals reconstruction,a novel reconstruction model based shift strategy in graph spectral domain is proposed in this paper,and it models the identity invariance of graph spectral band-limited components as a least-square problem.For solving the established reconstruction model,two novel reconstruction methods are proposed based on spectral shift operator and residual spectral shift operator.Compared with other methods,the novel methods improve iteration efficiency and reconstruction accuracy.Besides,the novel methods are suitable for the problem of separate band-limited graph signals reconstruction and have good performances.The simulation shows that compared with other reconstruction methods of band-limited graph signals,the novel methods improve about seventy percent in iterative efficiency and sixty percent of reconstruction accuracy.

关 键 词：图信号处理 信号重构 图谱理论 位移算子 

分 类 号：O157.5[理学—数学] TP18[理学—基础数学]