Conventional compressive beamforming assumes that the acoustic sources fall on the discretized grid points. The performance degrades when the acoustic source lies off the discretized grid point, that is, when the basis mismatch occurs. This paper proposes a two-dimensional Newtonized orthogonal matching pursuit compressive beamforming, including single and multiple snapshot versions, which constructs the maximum likelihood estimation model, taking the position and strength of sources on a two-dimensional continuous plane as parameters. This method first captures the grid point near the source based on the discrete grid. Then it optimizes the coordinate estimation within the local continuous plane by a combination of the two-dimensional Newton optimization and a feedback mechanism to converge to the actual source position. It allows acoustic source identification in the near field utilizing arbitrary geometry planar array and works without the prior knowledge of signal-to-noise ratio and/or regularization parameters. Simulations and experiments show that the proposed method can overcome the basis mismatch issue and provide high spatial resolution, obtaining an accurate estimation for the position and strength of the acoustic source. Moreover, the multiple snapshot version outperforms the single snapshot version, especially under low signal-to-noise ratio. The larger the number of snapshots, the better the performance.
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