Acoustic sources mapping based on the non-negative L_1/2 regularization

Phased microphone array techniques for estimating source locations and strengths have been widely employed in aeroacoustic applications. Many source localization algorithms by conducting the convex L₁ norm optimization have been proposed by assuming a spatially sparse distribution of the sound sources in recent years. Nevertheless, L₁ norm optimization has been shown to be suboptimal and cannot enforce further sparsity. This paper proposes a nonconvex L_1/2 regularization approach for solving the inverse problem of deconvolution approach to improve its spatial resolution and robustness. Thus, the iteratively reweighted least squares method is employed to solve the L_1/2 regularization problem. The capabilities of the proposed algorithm are demonstrated using various synthesized simulations to compare the results with other algorithms and it is found that multiple closely spaced sound sources with unequal powers can be identified. It indicates that the L_1/2 regularization method can provide significant improvement with high spatial resolution and reduced sidelobes compared to the L₁norm regularization method, and the computation cost is not increased significantly. The proposed method is applied in the experimental applications of benchmark test DLR1. Two incoherent sources are discerned near the flap side edge at particular frequency.