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

Abstract

Acoustic imaging is a powerful technique to localize and reconstruct source powers using microphone array, but it often involves timeconsuming and ill-posed inverse problems. In this paper, we propose to efficient build up the forward model of acoustic power propagation by using the convolution with the spatially invariant kernel. And kernel size and values are appropriately derived from the Symmetric Toepliz Block Toepliz of propagation matrix. For inverse problem, we then propose to apply hierarchical Variational Bayesian inference in order to achieve robust acoustic imaging in the colored background noises; Student's-t prior is explored to enforce the sparse distribution of acoustic powers and to obtain super resolution; moreover, wide dynamic range of estimated powers can be obtained thanks to the heavy tail of Student'st distribution; To achieve robust estimations, colored noise distributions are also modeled by the Student's-t prior, which does not excessively penalize large errors as the Gaussian prior does. Finally the proposed approach is compared with classical methods on the real data from wind tunnel experiments.

Aero-acoustics source separation with sparsity inducing priors in the frequency domain

“…In particular, the prediction of positions and absolute power levels is an important challenge for the aeronautic industry during the development of a new aircraft, mainly to reduce annoying noises around airports and in urban areas. The problem of discovering the location of noise sources and estimating the power levels has been efficiently solved using deconvolution based methods [1,2] but the characterization and separation of the noise sources is still an open problem. This characterization in the time domain is very important as it would allow a better understanding of the physical processes generating the noise.…”