| Graph signal processing is an effective tool for processing irregular graph domain data,and graph topology is an important component of graph signal processing.In existing graph signal studies,the graph topology is either completely known;or completely unknown and inferred from data observation.However,in reality,there is imperfect information about the graph topology.For example,in wireless communication networks,the topology is known,but there is a probability that some links will break due to random blocking or fading,in which case it can only be assumed that a ’base’graph is known,and that the graph will have a perturbation in its topology due to the failure of a small number of edges,and that the perturbation is probabilistic a priori.Based on the above,this paper investigates the sampling,quantization and filter design of graph signals under perturbation,with the following main tasks.(1)To address the problem of designing graph filters that are robust to quantization data and topological perturbations for practical applications where graph filter performance is affected by perturbations occurring in the topology of the graph with accumulated quantization errors during interest transmission,leading to large differences in filter output relative to expectations.An optimisation method is proposed to solve the problem using a convex optimisation problem that not only reduces the filter output error due to local perturbations in the graph topology,but also takes into account the quantization error in the graph filter iteration.(2)To address the impact of edge perturbations on the frequency domain analysis of the graph signal when small perturbations exist in the graph topology,and the impact of quantization on signal reconstruction,a signal estimation method with robustness to perturbations in the graph topology is derived using the probability of possible perturbations at the perturbed edges.And based on this,the effect of quantization error is reduced through the rate allocation of the node sample set,and an optimal rate allocation is sought through a greedy algorithm with a restricted quantization rate. |
