  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.
