Abstract
Beamforming is a powerful technique to achieve acoustic imaging in far-field. However, its spatial resolution is strongly blurred by the point spread function (PSF) of phased microphone array. Due to the limitation of array aperture and microphone density, the PSF is far from Dirac delta function, so that it is difficult to obtain a high-resolution beamforming image at low-frequencies (e.g.500-1500Hz). This paper proposes a Bayesian inference method based on Non-synchronous Array Measurements (Bi-NAM) so as to refine the PSF and break through the beamforming limitation for low-frequency source imaging. Firstly, by sequentially moving prototype array at different positions, the non-synchronous measurements can get a sizeable synthetic aperture and high density of microphones. The synthetic cross-spectrum matrix (CSM) can significantly improve the beamforming performance. To confine the approximation error of synthetic CSM and the uncertainty of forward model, as well as the noise interference, a Bayesian inference based on joint maximum a posterior (JMAP) is proposed to solve an ill-posed inverse problem. A Student-t prior is employed to enforce the sparse property of acoustic strength distribution. The background noise can be adaptively modeled by the Student-t distribution, which is related to some of the typical symmetric distributions. Then the hyper-parameters in JMAP inference are efficiently estimated by the Bayesian hierarchical framework. Through experimental data, the proposed Bi-NAM approach is confirmed to achieve high-resolution acoustic imaging at 1000Hz and 800Hz, respectively, even under the Laplace noise interference.
Highlights
Acoustic source imaging has widespread applications such as city-noise mapping, industry noise monitoring and mechanical fault diagnosis, etc
PROPOSED CONVOLUTION APPROXIMATION To make an insight on the point spread function (PSF) influence at the nonsynchronous measurement beamforming, we propose a convolution model to approximate the forward model of power propagation in (14)
This paper presents that the PSF of microphone array is a critical factor that causes quite blurred imaging for acoustic localization and visualization at low-frequencies
Summary
Acoustic source imaging has widespread applications such as city-noise mapping, industry noise monitoring and mechanical fault diagnosis, etc. B. FORWARD MODEL OF POWER PROPAGATION Based on the assumption of incoherent monopole sources, the full CSM RCSM can be expressed as: RCSM = GE Sl (Sl )H GH + E El (El )H. n=1 where El = (E{l1}, · · · , El{z}, · · · , E{lZ})T ∈ RMZ×1 denotes the model uncertainty of sequential measurements and noise interference at Z array positions, whose item E{lz} is defined in (5). Bayesian hierarchical diagram: y means beamforming map based on non-synchronous measurements, x means ground-truth of acoustic source power, and e means model uncertainty, including array noise interference and approximation error. Αx0 , βx0 , αe0 and βe0 are initialized by a random number between 0 and
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