Array measurements can be contaminated by strong noise, especially when dealing with microphones located near or in a flow. The denoising of these measurements is crucial to allow efficient data analysis or source imaging. In this paper, a denoising approach based on a Probabilistic Factor Analysis (PFA) is proposed. It relies on a decomposition of the measured cross-spectral matrix (CSM) using the inherent correlation structure of the acoustical field and of the flow-induced noise. This method is compared with three existing approaches, aiming at denoising the CSM, without any reference or background noise measurements and without any information about the sources of interest. All these methods make the assumption that the noise is statistically uncorrelated over the microphones, and only one of them significantly impairs the off-diagonal terms of the CSM. The main features of each method are first reviewed, and their performances are then evaluated by way of numerical simulations along with measurements in a closed-section wind tunnel.