Structured sublinear compressive sensing via belief propagation

TL;DR

This paper introduces a structured compressive sensing framework using graph codes, enabling efficient reconstruction algorithms with logarithmic complexity and near-optimal performance, suitable for practical sparse data acquisition.

Contribution

It presents a novel graph code-based structured sensing scheme with new belief propagation algorithms for fast and effective sparse signal reconstruction.

Findings

Reinforced belief propagation schemes achieve good complexity-performance tradeoffs.

Structured sensing matrices with graph codes perform near optimally with OMP.

Logarithmic-complexity algorithms outperform traditional methods in sparse scenarios.

Abstract

Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with Orthogonal Matching Pursuit (OMP) methods. For more elaborate greedy reconstruction schemes, we propose a new family of list decoding belief propagation algorithms, as well as reinforced- and multiple-basis belief propagation algorithms. Our simulation results indicate that reinforced BP CS schemes offer very good complexity-performance tradeoffs for very sparse signal vectors.