Block-sparse beamforming for spatially extended sources in a Bayesian formulation

Abstract

Direction-of-arrival (DOA) estimation refers to the localization of sound sources on an angular grid from noisy measurements of the associated wavefield with an array of sensors. For accurate localization, the number of angular look-directions is much larger than the number of sensors, hence, the problem is underdetermined and requires regularization. Traditional methods use an ℓ2-norm regularizer, which promotes minimum-power (smooth) solutions, while regularizing with ℓ1-norm promotes sparsity. Sparse signal reconstruction improves the resolution in DOA estimation in the presence of a few point sources, but cannot capture spatially extended sources. The DOA estimation problem is formulated in a Bayesian framework where regularization is imposed through prior information on the source spatial distribution which is then reconstructed as the maximum a posteriori estimate. A composite prior is introduced, which simultaneously promotes a piecewise constant profile and sparsity in the solution. Simulations and experimental measurements show that this choice of regularization provides high-resolution DOA estimation in a general framework, i.e., in the presence of spatially extended sources.

Sound source localization and speech enhancement with sparse Bayesian learning beamforming

“…[9][10][11][12] While ' pnorm regularized maximum likelihood methods, with p 1, have been proposed to promote sparsity in DOA estimation [9][10][11]13 and wavefield reconstruction, 14,15 the accuracy of the resulting sparse estimate is determined by the ad hoc choice of the regularization parameter. 12,16 Sparse Bayesian learning (SBL) is a probabilistic parameter estimation approach which is based on a hierarchical Bayesian method for learning sparse models from possibly overcomplete representations resulting in robust maximum likelihood estimates. 17,18 Specifically, the Bayesian formulation of SBL allows regularizing the maximum likelihood estimate with prior information on the model parameters.…”

Sequential adaptive elastic net approach for single-snapshot source localization

“…Next we turn our attention on how to choose the adaptive (i.e., data dependent) weights in c-PW-WEN. In adaptive Lasso 20 , one ideally uses the LSE or, if p > n, the Lasso as an initial estimatorβ init to construct the weights given in (4). The problem is that both the LSE and the Lasso estimator have very poor accuracy (high variance) when there exists high correlations between predictors, which is the condition we are concerned in this paper.…”

In-Depth Exploration of Signal Self-Cancellation Phenomenon to Achieve DOA Estimation of Underwater Acoustic Sources

“…In the least absolute shrinkage and selection operator (LASSO) method [18], the signal amplitude vector is obtained by solving an l 1 -norm regularized least-squares problem. The LASSO method contains the l 1 -norm constraint on the solution vector, thus making the result of the solution vector sparse [19]. By linear transformation of the solution vector, the weighted LASSO method [20] imposes certain structural constraint on the solution vector to achieve efficient processing of spatially extended sources (e.g., underwater embedded objects in acoustic imaging [21]).…”

“…By linear transformation of the solution vector, the weighted LASSO method [20] imposes certain structural constraint on the solution vector to achieve efficient processing of spatially extended sources (e.g., underwater embedded objects in acoustic imaging [21]). The total variation norm regularization method [22] for DOA estimation of spatially extended sources can be seen as a special case of the weighted LASSO method, which uses the band matrix to realize the linear transformation of the solution vector, so that the solution vector has block sparsity [19,23]. Besides, using the information contained in the covariance matrix, the sparse spectrum fitting (SpSF) algorithm [24] first performs a vectorization operation on the covariance matrix, and then fits the estimated covariance matrix and the ideal covariance matrix under the l 2 -norm.…”