Acoustical source reconstruction from non-synchronous measurements by Gibbs sampling

Acoustical source reconstruction from non-synchronous measurements is a powerful method for achieving large arrays and/or high microphone density by scanning the object of interest from a sequential movement of an arbitrary prototype array. It has attracted great interests recently, since it is beyond the fundamental limitation of working frequency that is determined by the size and microphone density of an array. The problem of the non-synchronous measurements of microphone array boiled down to a matrix completion of a block diagonal spectral matrix. In this paper, the problem of non-synchronous measurements has been investigated in the Bayesian formalism. First, a statistical forward model of non-synchronous measurements is constructed; second, the spectral matrix completion is implemented based on the the Gibbs sampling. In the numerical experiments, convergence diagnosis of Markov chain is illustrated through two approaches (i.e. trace plot and ergodic mean plot).