Phase Transition Analysis of Sparse Support Detection from Noisy Measurements

TL;DR

This paper compares Bayesian hypothesis test via belief propagation (BHT-BP) with CS-BP for sparse support detection, showing BHT-BP's superior robustness against noise through phase transition analysis and experimental validation.

Contribution

It introduces a phase transition analysis for BHT-BP in sparse support detection and demonstrates its robustness over estimation-based algorithms like CS-BP.

Findings

BHT-BP outperforms CS-BP in noise robustness.

Phase transition analysis specifies detection thresholds.

Experimental results validate the analytical phase transition predictions.

Abstract

This paper investigates the problem of sparse support detection (SSD) via a detection-oriented algorithm named Bayesian hypothesis test via belief propagation (BHT-BP). Our main focus is to compare BHT-BP to an estimation-based algorithm, called CS-BP, and show its superiority in the SSD problem. For this investigation, we perform a phase transition (PT) analysis over the plain of the noise level and signal magnitude on the signal support. This PT analysis sharply specifies the required signal magnitude for the detection under a certain noise level. In addition, we provide an experimental validation to assure the PT analysis. Our analytical and experimental results show the fact that BHT-BP detects the signal support against additive noise more robustly than CS-BP does.