A Noise-Robust Method with Smoothedℓ1/ℓ2Regularization for Sparse Moving-Source Mapping

Abstract

The method described here performs blind deconvolution of the beamforming output in the frequency domain. To provide accurate blind deconvolution, sparsity priors are introduced with a smoothed 1 / 2 regularization term. As the mean of the noise in the power spectrum domain depends on its variance in the time domain, the proposed method includes a variance estimation step, which allows more robust blind deconvolution. Validation of the method on both simulated and real data, and of its performance, are compared with two well-known methods from the literature: the deconvolution approach for the mapping of acoustic sources, and sound density modeling.

A High-Resolution and Low-Frequency Acoustic Beamforming Based on Bayesian Inference and Non-Synchronous Measurements

“…In (13) and (4), the beamforming output y n 1 at the n 1 -th grid mainly depends on the weighted combination of all discrete power vector x and its weight h n 1 ,n 2 , which comes from each row of the power propagation matrix H. In (14), the CBF result y of non-synchronous measurements depends on the weighted combinations (Hx) of all discrete grids. Then the source power x can be estimated from an inverse problem in (14) when given y under model uncertainty e.…”

“…To make an insight on the PSF influence at the nonsynchronous measurement beamforming, in this section, we propose a convolution model to approximate the forward model of power propagation in (14). We find out that power propagation matrix H seems to be a quasi-Symmetric Block Toeplitz (SBT) matrix in the far-field measurement, so that…”

“…For a stochastically stationary process, the Gaussian distribution is regarded as the most common prior to the unknown variables. The Gaussian priors are assigned to model uncertainty in (14) or (15): each component of e is approximated as a zero-mean Gaussian distribution with unknown variance v e and all the elements of e are independent of each other. The rationality of this assumption is detailed in the reference [3], [14], [19], [29].…”

“…The Gaussian priors are assigned to model uncertainty in (14) or (15): each component of e is approximated as a zero-mean Gaussian distribution with unknown variance v e and all the elements of e are independent of each other. The rationality of this assumption is detailed in the reference [3], [14], [19], [29]. Therefore the prior distribution of e and likelihood function can be expressed as: (20) where N (0, v e ) stands for Gaussian independent distribution.…”

“…So that the power distribution of acoustic sources is sparsely distributing along the scanning plane. This sparsity is an essential constraint for solving the inverse problem of (14). From the perspective of the Bayesian framework, Probability Density Function (PDF) is the most intuitive representation of the sparsity of prior information.…”