As a powerful tool, near-field acoustical holography (NAH) recognizes the sound source effectively. The traditional equivalent source method (ESM) calculated by the Tikhonov regularization method could be available in the low-frequency band. To improve the resolution quality of traditional ESM in the middle-frequency band and the high-frequency band, we introduced a fast iterative shrinkage/thresholding algorithm via Laplace norm for sound source identification based on the equivalent source method (LFISTA). In this paper, four methods including the Tikhonov regularization method, the monotonic two-step iterative shrinkage/thresholding (MTwIST), the fast iterative shrinkage/thresholding algorithm (FISTA), and the proposed method were compared for evaluation of performance. Both of the simulated and experimental results indicated that the proposed method identified the targeted sound sources in the entire frequency range more precisely than the Tikhonov regularization method did; the proposed method fixed the problem that MTwIST had the unqualified resolution and unstableness in the low-frequency band.

中文翻译：

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一种通过拉普拉斯范数进行声源识别的快速迭代收缩/阈值算法

作为一种强大的工具，近场声全息 (NAH) 可以有效地识别声源。Tikhonov正则化方法计算的传统等效源法（ESM）在低频段可用。为了提高传统ESM在中频段和高频段的分辨率质量，我们引入了一种基于等效源法（LFISTA）的通过拉普拉斯范数进行声源识别的快速迭代收缩/阈值算法。在本文中，对包括 Tikhonov 正则化方法、单调两步迭代收缩/阈值（MTwIST）、快速迭代收缩/阈值算法（FISTA）在内的四种方法以及所提出的方法进行了性能评估。仿真和实验结果均表明，与Tikhonov正则化方法相比，该方法在整个频率范围内更准确地识别了目标声源；该方法解决了MTwIST在低频段分辨率不合格和不稳定的问题。