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In this study, a hybrid compressive sensing reconstruction algorithm called SAMP-CoSaMP is proposed. The unique combination maintains the speed advantage of CoSaMP and the adaptive sparsity searching ability from the SAMP. Afterwards, an improved beamforming algorithm named SC-DAMAS for sound source localisation is created by integrating our hybrid algorithm with the classic DAMAS. Lastly, the reconstruction accuracy is compared between the SAMP-CoSaMP, SAMP, and CoSaMP algorithms in different signal-to-noise ratio scenarios. The results show that the SAMP-CoSaMP is balanced between running efficiency and reconstruction error. In addition, we perform comparative sound source localisation simulations and experiments by our SC-DAMAS with those of the conventional beamforming method and orthogonal matching pursuit algorithm-based deconvolution approach. SC-DAMAS is superior to the aforementioned counterparts in localisation performance without the need to predetermine the sparsity value.

In order to improve the accuracy of the sparse regularization equivalent source acoustic holography algorithm, based on the analysis of the holographic algorithm theory, an optimized array arrangement is proposed. The sensing matrix constructed by the array parameters directly affects the accuracy of the acoustic imaging algorithm. By analyzing the influence of the sensing matrix on the imaging algorithm, the Restricted Isometry Constant (RIC) is chosen to evaluate the sensing matrix. Using genetic algorithm (GA), the RIC is taken as the fitness value, and the optimal pseudo-random array is selected and compared with the conventional array arrangement for acoustic imaging. Experiments show that the optimized pseudo-random array has better imaging effect under the same number of sensor measurements, and provides an optimization method for the design of acoustic array.

The compressive-equivalent source method near-field acoustic holography (C-ESM) is disturbed by reverberation in the enclosed space such as room and cabin, which leads to large reconstruction error and disturbs the judgment of sound source position. In order to solve this problem, an improved C-ESM algorithm based on room impulse response (RIR) is proposed to filter out reverberation interference in this paper. Different from the original equivalent source method, the improved algorithm constructs the transfer function through the room impulse response to establish the relationship between the equivalent source and the sound pressure on any plane in space, and the sparse signal reconstruction method of the compressive sensing technology is used to obtain the strength of the equivalent source. Then the transfer function to any plane of space is established according to the free field Green’s function, to eliminate the interference of reverberation and improve the effect of sound source location. The accuracy and effectiveness of the improved method are verified by preliminary numerical simulation. And the results show that compared with the original algorithm, this method has obvious advantages in sound source localization in a reverberant field.

The mechanical noise in the cabin of the ship is so large that the leakage of high-pressure fluid is not easily noticed. In view of this situation, a near-field acoustic holography for high-frequency weak sound source under low signal-to-noise ratio is proposed. The method uses the empirical mode decomposition method to add weights to the time-domain sampling signals of each array element, and then uses the plane equivalent source near-field acoustic holography combined with compressive sensing to find the holographic surface acoustic pressure distribution. The simulation and experiment show that this method has certain feasibility under low signal-to-noise ratio, and the results are better than the method based on Fourier transform and the traditional boundary element method. It is of positive significance to apply it to engineering practice.