Graph Signal Compression by Joint Quantization and Sampling

Graph signals arise in various applications, ranging from sensor networks to social media data. The high-dimensional nature of these signals implies that they often need to be compressed in order to be stored and transmitted. The common framework for graph signal compression is based on sampling, resulting in a set of continuous-amplitude samples, which in turn have to be quantized into a finite bit representation. In this work, we study the joint design of graph signal sampling along with quantization, for graph signal compression. We focus on bandlimited graph signals, and show that the compression problem can be represented as a task-based quantization setup, in which the task is to recover the spectrum of the signal. Based on this equivalence, we propose a joint design of the sampling and recovery mechanisms for a fixed quantization mapping, and present an iterative algorithm for dividing the available bit budget among the discretized samples. Furthermore, we show how the proposed approach can be realized using graph filters combining elements corresponding the neighbouring nodes of the graph, thus facilitating distributed implementation at reduced complexity. Our numerical evaluations on both synthetic and real world data shows that the joint sampling and quantization method yields a compact finite bit representation of high-dimensional graph signals, which allows reconstruction of the original signal with accuracy within a small gap of that achievable with infinite resolution quantizers.