Joint System Design And Optimization Of Graph Signal Sampling And Quantization Under Total Bits Limitation

How to effectively deal with the generation of a large number of signals and process the massive data has become a crucial issue.As a signal processing method that can effectively use data structure information,graph signal processing is getting more and more attention.At the same time,scalar quantization and vector quantization methods play an important role in traditional signal processing field.In this dissertation,two schemes of the sampled graph signal quantization system are proposed,combining the weighted random sampling scheme of the graph signal.One is a scalar quantization scheme for sampled graph signals,and the other is a vector quantization scheme for sampled graph signals.Considering the rate restriction due to ubiquitous memory,power consumption or communication environment limitations in the actual situation,this dissertation will impose the restriction of total number of bits on the two sampled graph signal quantization systems.The purpose of the two schemes is to effectively compress the graph signal under a certain limitation of the total number of bits.The performance level of these two systems can be measured by reconstructing the compressed graph signal and calculating the distortion of the reconstructed signal relative to the original signal.In addition,this dissertation will further optimize or improve the two systems from the perspective of improving the distortion performance of these two systems.In the scalar quantization system of sampled graph signals,this dissertation proposes an optimal uniform quantization bit allocation scheme by using information obtained in sampling procedure,which is convenient to access in such an joint design system.The optimality of this allocation scheme is then proved.After that,in order to reduce the computational complexity of this optimal solution,this dissertation also proposes an efficient bit allocation scheme.Through simulation experiments on three graphs,the effectiveness of these two allocation schemes under the condition of low bit number limitation is demonstrated.Compared with the scalar quantization scheme,the vector quantization system has advantages in both distortion and flexibility.This dissertation proposes two sampled graph signal vector quantizers,one of which is a random codebook vector quantizer,and the other is a combinatorial uniform codebook vector quantizer.Considering the limitation of the total number of bits,this dissertation also proposes two novel vector quantization bit allocation schemes.Different from the bit allocation based on the dimension of the clustering vector,one of these two allocation schemes is based on the concept of"maximum aggregation property of graph energy" of cluster proposed in this dissertation,and the other is based on the comprehensive consideration of both dimension and the maximum aggregation property of graph energy of cluster.The simulation results show that these two schemes have better distortion performance compared to the bit allocation scheme based on the dimensions of cluster.