Two-dimensional sparse Bayesian learning compressive beamforming with planar microphone array for acoustic source identification

Two-dimensional (2D) compressive beamforming (CB) with planar microphone array for acoustic source identification has attracted much attention due to its advantages of wide identification space, applicability to both coherent and incoherent acoustic sources, and clear imaging. It realizes acoustic source identification by establishing and solving the underdetermined equations between the sound pressure measured by the microphone array and the source strengths of the discretized grid points in the target area. Convex relaxation algorithms and greedy algorithms are often used to solve these underdetermined equations. CB based on convex relaxation requires the sensing matrix to satisfy the restricted isometry property and needs large calculating consumption, which is unsuitable for large-scale problems. CB based on greedy algorithms may achieve a locally optimal solution instead of the global optimum, and it is easily affected by the coherence of the sensing matrix columns, so its performance is sensitive to the grid spacing. To take into account both the robustness of acoustic source identification performance and high computational efficiency, we adapted sparse Bayesian learning (SBL) to solve the above underdetermined equations and proposed a 2D-SBL-CB in this paper. It first assumes the signal prior and noise prior to derive the posterior probability distribution of the source strength, and then adaptively estimates the hyperparameters of the sparse prior of source strength based on a type-II maximum likelihood, i.e., by maximizing the evidence, to achieve source identification. Both simulations and experiment show that the proposed 2D-SBL-CB is robust to grid spacing and has stable source identification performance. It also enjoys high computational efficiency, strong spatial resolution ability, and strong anti-noise interference, with optimal overall performance.