# Task-Based Graph Signal Compression

arXiv: https://arxiv.org/abs/2110.12387 · HTML: https://mlsanity.com/paper/2110.12387/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 38 references that are in the map.
- First posted on arXiv 24 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [UVeQFed: Universal Vector Quantization for Federated Learning](https://mlsanity.com/paper/2006.03262/) (2020)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Discrete Signal Processing on Graphs: Sampling Theory](https://mlsanity.com/paper/1503.05432/) (2015)
- [Learning Sparse Graphs Under Smoothness Prior](https://mlsanity.com/paper/1609.03448/) (2016)
- [Deep Task-Based Quantization](https://mlsanity.com/paper/1908.06845/) (2019)
- [Greedy Sampling of Graph Signals](https://mlsanity.com/paper/1704.01223/) (2017)
- [Asymptotic Task-Based Quantization with Application to Massive MIMO](https://mlsanity.com/paper/1811.10077/) (2018)
- [Task-Based Analog-to-Digital Converters](https://mlsanity.com/paper/2009.14088/) (2020)
- [Generalized Sampling on Graphs With Subspace and Smoothness Priors](https://mlsanity.com/paper/1905.04441/) (2019)
- [Task-Based Quantization with Application to MIMO Receivers](https://mlsanity.com/paper/2002.04290/) (2020)
- [A Markov Variation Approach to Smooth Graph Signal Interpolation](https://mlsanity.com/paper/1806.03174/) (2018)
- [Sampling Signals on Graphs: From Theory to Applications](https://mlsanity.com/paper/2003.03957/) (2020)

## Built on by (most cited first, 1 of 1)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)

## Abstract (arXiv)

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.