Error Feedback Approach for Quantization Noise Reduction of Distributed Graph Filters

TL;DR

This paper presents an error feedback method inspired by digital filter techniques to effectively reduce quantization noise in distributed graph filters across various topologies.

Contribution

It introduces a novel error feedback approach that connects quantized filtering with error spectrum shaping, providing theoretical analysis and closed-form error coefficients.

Findings

Significant noise reduction in distributed graph filters

Effective across deterministic and random topologies

Theoretical derivation of error spectrum shaping for graph filters

Abstract

This work introduces an error feedback approach for reducing quantization noise of distributed graph filters. It comes from error spectrum shaping techniques from state-space digital filters, and therefore establishes connections between quantized filtering processes over different domains. Quantization noise expression incorporating error feedback for finite impulse response (FIR) and autoregressive moving average (ARMA) graph filters are both derived with regard to time-invariant and time-varying graph topologies. Theoretical analysis is provided, and closed-form error weight coefficients are found. Numerical experiments demonstrate the effectiveness of the proposed method in noise reduction for the graph filters regardless of the deterministic and random graph topologies.