提出一种可用于相干声源识别的快速反卷积声源成像算法（Fast deconvolution approach for the mapping of coherent acoustic sources，FC-DAMAS）。该算法去除了反卷积声源成像算法（Deconvolution approach for the mapping of acoustic sources，DAMAS）中的互谱过程，直接求解声源复数源强分布，从而避免了互谱操作导致的待求未知数个数的剧增，因此不再需要采用非相干声源假设来减少待求未知数，使该算法能够同时适用于相干和非相干声源的识别；其次，该算法在反卷积求解过程中采用了与稀疏约束反卷积声源成像算法（Sparsity constrained DAMAS，SC-DAMAS）类似的L1范数稀疏约束反卷积方法，使算法在相干和非相干声源的识别过程中均具有很高的计算精度和空间分辨率；此外，该算法中增加了对测量声压的主成分分析去噪过程，弥补了取消互谱去噪过程造成的算法鲁棒性下降，使算法具有与SC-DAMAS算法类似的噪声鲁棒性。与现有可用于相干声源识别的反卷积声源成像算法（Deconvolution approach for the coherent sources，DAMAS-C）相比，提出的FC-DAMAS算法大大降低了待求解的矩阵方程规模，使其计算效率得到了显著提升。通过数值仿真和实验验证了FC-DAMAS算法的优越性，结果表明所提出的FC-DAMAS算法在应用范围、声源识别性能和实用性方面都更具优势，更适于在实际工程中应用。
A fast deconvolution approach for the mapping of coherent acoustic sources (FC-DAMAS) is proposed in the paper. The approach eliminates the cross spectrum process in the DAMAS and directly solves the complex strength of the sound source, which avoids the increase of the number of unknowns caused by the cross-spectrum operation. Therefore, it is no longer necessary to use the non-coherent source hypothesis to reduce the number of unknowns, so that the algorithm can be applied to both coherent and non-coherent sources Secondly, the approach uses the L1 norm sparse constrained deconvolution method similar to the sparsity constrained DAMAS approach(SC-DAMAS), which makes the approach has high computational precision and spatial resolution in the identification process of coherent and non-coherent sound sources. In addition, a principal component analysis de-noising process applied to the measured sound pressure is added in the proposed approach, which compensates the aberration of the algorithm caused by canceling the cross-spectrum de-noising process and so that the approach has similarity to the noise robustness of the SC-DAMAS. Furthermore, compared with the deconvolution approach for the coherent sources (DAMAS-C), the proposed FC-DAMAS greatly reduces the scale of the matrix equation to be solved, so that its computational efficiency is improved significantly. In this paper, the advantages of FC-DAMAS are verified by numerical simulation and experiment. The results show that the proposed FC-DAMAS has advantages in terms of application range, sound source recognition performance and practicability, and is more suitable for practical application.
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