Bayesian Compressive Sensing via Belief Propagation

TL;DR

This paper introduces a Bayesian compressive sensing method using belief propagation, enabling efficient decoding of sparse signals with fewer measurements and adaptable to various signal models.

Contribution

It presents a novel belief propagation-based Bayesian inference approach for compressive sensing that reduces computational complexity and measurement requirements.

Findings

Uses O(Klog(N)) measurements for decoding sparse signals.

Achieves O(Nlog^2(N)) computational complexity.

Easily adaptable to different signal models.

Abstract

Compressive sensing (CS) is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable, sub-Nyquist signal acquisition. When a statistical characterization of the signal is available, Bayesian inference can complement conventional CS methods based on linear programming or greedy algorithms. We perform approximate Bayesian inference using belief propagation (BP) decoding, which represents the CS encoding matrix as a graphical model. Fast computation is obtained by reducing the size of the graphical model with sparse encoding matrices. To decode a length-N signal containing K large coefficients, our CS-BP decoding algorithm uses O(Klog(N)) measurements and O(Nlog^2(N)) computation. Finally, although we focus on a two-state mixture Gaussian model, CS-BP is easily adapted to other signal models.