Sound Source Reconstruction with Gibbs Sampler from Non-Synchronous Wind Tunnel Measurements

In conventional array signal processing, the resolution of acoustic imaging and the working frequency of the array are directly limited by the aperture and density of the microphone array due to Rayleigh limit. One solution is to sequentially scan the object through a prototype array to synthesize a large aperture or higher-density array, which is referred to as non-synchronous measurements (NSM). A fundamental problem in the NSM is the recovery of the missing phase relations between consecutive measurements compared to synchronous measurements (SM), and this problem is deemed as the matrix completion problem of a block diagonal spectral matrix. In this work, acoustic source reconstruction from NSM is considered as the problem of solving a system of equations (inverse acoustical problem). Bayesian inference based on Gibbs sampling is proposed to solve the ill-posed inverse problem. Sources strength distribution and noise are modeled as a Bayesian hierarchical framework solved by sampling in the posterior probability density functions (PDF). The proposed method is validated effectively by numerical simulations and wind tunnel test experiments.