Robust Bayesian super-resolution approach via sparsity enforcing a priori for near-field aeroacoustic source imaging

Abstract

Near-field aeroacoustic imaging has been the focus of great attentions of researchers and engineers in aeroacoustic source localization and power estimation for decades. Recently the deconvolution and regularization methods have greatly improved spatial resolution of the beamforming methods. But neither are they robust to background noises in the low Signal-to-Noise Ratio (SNR) situation, nor do they provide a wide dynamic range of power estimation. In this paper, we first propose an improved forward model of aeroacoustic power propagation, in which, we consider background noises and forward model uncertainty for the robustness. To solve the inverse problem, we then propose a robust Bayesian super-resolution approach via sparsity enforcing a priori. The sparse prior of source powers can be modeled by double exponential distribution, which can improve the spatial resolution and promote wide dynamic range of source powers. Both the hyperparameters and source powers can be alternatively estimated by the Bayesian inference approach based on the joint Maximum A Priori optimization. Finally our Bayesian approach is compared with some of the state-of-the-art methods on simulated, real and hybrid data. The main advantages of our approach are of robustness to noise, a wide dynamic range, super spatial resolution, and non-necessity for prior knowledge of the source number or SNR. It is feasible to apply it for aeroacoustic imaging with the 2D non-uniform microphone array in wind tunnel tests, especially for near-field monopole and extended source imaging.

An efficient variational Bayesian inference approach via Studient's-t priors for acoustic imaging in colored noises

“…We also apply the equivalent sources and mirror sources to correct the wind refraction and ground reflection respectively as discussed in authors' paper [5].…”

“…Wind tunnel experiments: (a) Wind tunnel S2A [7] and (b) Illustration of signal processing [5] Here we want to reveal that propagation matrix C would be the Symmetric Toeplitz-Block-Toeplitz (STBT) matrix under two natural approximations: For any i j ∈ {1, ··· , N}, we have a i …”

“…And such a sparse distribution can be represented by a centralized PDF function that has a very high value around the original zero (sparsity) and a long heavy tail (dynamic range of source powers), such as Laplacian priors [4] and Student's-t priors [9]. Recently, the authors have proposed to apply Double Exponential DE (x) priors based on JMAP for robust super resolution acoustic imaging [5]. However, due to the complexity of JMAP, we propose to use the VB inference via Student's-t prior the to obtain the robust acoustic imaging in colored noises.…”

“…More recently, 1 sparse regularization has been investigated to greatly improve the spatial resolutions [4]. The authors have proposed several approaches by making good use of sparse distribution of source powers in Gaussian white noises, such as Robust DAMAS with Sparse Constraint (SC-RDAMAS), Bayesian inference approach via a sparsity enforcing prior [5].…”

Inverse problem with beamforming regularization matrix applied to sound source localization in closed wind-tunnel using microphone array

“…The spatial resolution of this approach is increased but the computation time is large due to the iterative nature of the method. New methods based on sparsity constraint [8] or Bayesian approach [9] allow super-resolution in acoustic imaging, but the computation time is very large and these methods use dedicated toolbox to solve the inverse problem.…”