Robust Acoustic Imaging Based on Bregman Iteration and Fast Iterative Shrinkage-Thresholding Algorithm

The acoustic imaging (AI) technique could map the position and the strength of the sound source via the signal processing of the microphone array. Conventional methods, including far-field beamforming (BF) and near-field acoustic holography (NAH), are limited to the frequency range of measured objects. A method called Bregman iteration based acoustic imaging (BI-AI) is proposed to enhance the performance of the two-dimensional acoustic imaging in the far-field and near-field measurements. For the large-scale ${\ell }_1$ norm problem, Bregman iteration (BI) acquires the sparse solution; the fast iterative shrinkage-thresholding algorithm (FISTA) solves each sub-problem. The interpolating wavelet method extracts the information about sources and refines the computational grid to underpin BI-AI in the low-frequency range. The capabilities of the proposed method were validated by the comparison between some tried-and-tested methods processing simulated and experimental data. The results showed that BI-AI separates the coherent sources well in the low-frequency range compared with wideband acoustical holography (WBH); BI-AI estimates better strength and reduces the width of main lobe compared with ${\ell }_1$ generalized inverse beamforming (${\ell }_1$-GIB).