Graph Signal Compression via Task-Based Quantization

Abstract

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 conveyed. The common framework for graph signal compression is based on sampling, resulting in a set of continuousamplitude 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 the quantization of these samples, 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. Our numerical evaluations demonstrate that the proposed scheme achieves reconstruction accuracy within a small gap of that achievable with infinite resolution quantizers, while compressing high-dimensional graph signals into finite bit streams.Index terms-Graph signal compression, task-based quantization.

Task-Based Graph Signal Compression

“…In this section, we evaluate the performance of the proposed joint sampling and quantization methods for graph signal compression. 1 In Subsection V-A, we simulate graph signals representing measurements taken using parameters provided in GSP toolbox [37]. We then use the proposed scheme to compress graph signals representing real-world temperature data in Subsection V-B.…”

“…Throughput this section, we evaluate the MSE achieved when compressing the graph signal using to the following schemes: (1) Joint sampling and quantization with unconstrained filters via Algorithm 1; (2) Separate sampling and quantization with non-identical quantizers as in [20]; (3) the MMSE estimate achievable of U k c which is achievable 1 The source code used in this section is available online in the following link: https://github.com/Pei65536/Graph Signal Compression.git with infinite resolution quantization, i.e., without quantization constraints; (4) Joint sampling and quantization with identical quantizers as in [21]; and (5) Joint sampling and quantization with frequency domain graph filters via Algorithm 4.…”

“…Part of this work has been presented in the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2021 [1]. This work was supported in part by the National Natural Science Foundation of China under grant No 61971238, by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme, and by the Israel Science Foundation under grant No.…”

“…Then φ is Schur-convex (Schur-concave) on D n if and only if∂φ(x) ∂xi is decreasing (increasing) in i = 1, ..., n. Assume that Ḿi is the optimal bit allocation and άi is the corresponding diagonal elements satisfying {3 Ḿ 2 i /2η 2 } ≺ {ά i }. Denote M(1) = P i=1 log 2 3 Ḿ 2 i /2η 2 and M (2) =…”