Optimal Quantization for Compressive Sensing under Message Passing Reconstruction

TL;DR

This paper develops optimal scalar quantizers for compressive sensing measurements to improve signal reconstruction accuracy using relaxed belief propagation, with theoretical predictions and empirical validation.

Contribution

It introduces a method to design mean-square optimal quantizers tailored for relaxed BP in compressive sensing, enhancing reconstruction performance.

Findings

Quantizers designed via state evolution achieve lower reconstruction error.

Empirical results confirm the superiority of the proposed quantizers.

The approach effectively predicts and improves quantization performance.

Abstract

We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired by message passing algorithms on bipartite graphs. Its asymptotic error performance can be accurately predicted and tracked through the state evolution formalism. We utilize these results to design mean-square optimal scalar quantizers for relaxed BP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.