In this work, the difference convex function based on capped nuclear norm minimization (CNNM-DC) method, a cross-spectral matrix (CSM) completion iterative algorithm with excellent noise immunity, is proposed to realize acoustic imaging of non-synchronous measurements (NSM) under the condition of low signal-to-noise ratio (SNR). Compared with the CSM completion algorithm based on the nuclear norm minimization (NNM) model, the truncated nuclear norm regularization (TNNR) model, and the weighted nuclear norm minimization (WNNM) model, the proposed method can obtain the acoustic image with narrow main lobes and no sidelobe under the condition of low SNR. The simulation results show that, under conditions of low SNR, the proposed method effectively reduces the width of the main lobe, suppresses the side lobes, and achieves more accurate imaging results than the previous method. Finally, experiments were conducted to verify the feasibility of CNNM-DC. The experimental results show that the proposed method is an accurate acoustic imaging algorithm for NSM under low SNR, which lays a foundation for acoustic imaging in industrial occasions with strong background noise interference.

本文提出了基于上限核范数最小化的差分凸函数（CNNM-DC）方法，这是一种具有优异抗噪性的交叉谱矩阵（CSM）完成迭代算法，用于实现非同步测量（NSM）的声学成像）在低信噪比（SNR）条件下。与基于核范数最小化（NNM）模型、截断核范数正则化（TNNR）模型和加权核范数最小化（WNNM）模型的CSM补全算法相比，该方法可以获得主瓣较窄的声学图像且在低信噪比条件下无旁瓣。仿真结果表明，在低信噪比条件下，该方法有效减小了主瓣宽度，抑制了旁瓣，取得了比之前方法更准确的成像结果。最后通过实验验证CNNM-DC的可行性。实验结果表明，该方法是一种低信噪比下准确的NSM声学成像算法，为强背景噪声干扰的工业场合的声学成像奠定了基础。