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• Space-snapshot representation for acoustic imaging in a complex, noisy environment is investigated. • Low rank and Mixture of Gaussian modeling are proposed to achieve significant denoising performance. • Comparisons with other methods are made in simulations and experiments to verify the effect of the state-of-the-art methods. 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. [ABSTRACT FROM AUTHOR]

• Acoustic inverse problems in the framework of ADMM are investigated. • The iteration algorithms of ADMM in the complex domain have been derived. • ADMM has been systematically compared with the sparse holography. • Both simulation and experimentation have verified the performance of ADMM. Acoustic imaging is an important technique for sound source identification which is widely used in noise control and fault detection. It can be described as a method for reconstructing the amplitude and phase distribution of an acoustic field in a given plane. When the size of radiating object is huge and measurement environment is noisy, accuracy and efficiency of acoustic imaging algorithm deteriorate easily. In this paper, a novel computational framework is investigated to simplify the algorithm and balance computation speed with accuracy. It converts acoustic imaging into an inverse problem and then divides this problem into two parts including forward model and denoising model. This computation framework is based on the alternating direction method of multipliers, which makes parallel implementation and distributed optimization possible, especially for large scale measurements. It is assumed that the acoustic field is composed of a cluster of monopole sources and the equivalent source method is taken to solve the acoustic inverse problem. Both L 2 -norm penalization based on the minimal energy assumption and L p -norm (0 < p ⩽ 1) penalization based on the sparsity hypothesis are taken in this framework. Thus, the regularization parameter in the algorithm, which balances the standard least square error and the norm of the source solution, can be coupled with some pre-existing methods incluing L-curve, GCV and Bayesian strategies. Different regularization parameters are proposed and the comparison is made in this paper. The proposed method provides a general and convenient method for different type of sound source priors and it is validated with an experiment. [ABSTRACT FROM AUTHOR]