Low-rank Gaussian mixture modeling of space-snapshot representation of microphone array measurements for acoustic imaging in a complex noisy environment

The microphone array can simultaneously obtain the multi-dimensional information (space-time-frequency) of sound sources, which is recognized as a fundamental and powerful tool in acoustic imaging. Acoustic Beamforming is one of the widely used methods in acoustic imaging. However, most of the applications of beamforming are based on the Gaussian noise assumption, which is not always accurate in on-site measurements. For example, shock noise with a skewed probability density function (PDF) may appear on the signal record when the turbulent eddies are not controlled. Thus, in this paper, the conventional Gaussian noise model is extended to a Gaussian mixture noise model, which can approximate any probability distribution of the noise in theory. The space-snapshot representation of microphone array measurements is further modeled as a combination of the low-rank matrix part (measurements from the sound sources) and a Gaussian mixture matrix part (measurement noise). The signal from the sources of interest is finally recovered by the Expectation–maximization algorithm, which iterates between the low-rank approximation of the sound sources and the estimation of the parameter of the Gaussian mixture model. The proposed method is further investigated with simulations and compared with robust principal component analysis (RPCA) and Gaussian-based probabilistic factor analysis (PFA). It is concluded that the proposed method outperforms the state-of-the-art denoising methods.