A Robust and Efficient Compressed Sensing Algorithm for Wideband Acoustic Imaging

Abstract Wideband acoustic imaging, which combines compressed sensing (CS) and microphone arrays, is widely used for locating acoustic sources. However, the location results of this method are unstable, and the computational efficiency is low. In this work, in order to improve the robustness and reduce the computational cost, a DCS-SOMP-SVD compressed sensing method, which combines the distributed compressed sensing using simultaneously orthogonal matching pursuit (DCS-SOMP) and singular value decomposition (SVD) is proposed. The performance of the DCS-SOMP-SVD is studied through both simulation and experiment. In the simulation, the locating results of the DCS-SOMP-SVD method are compared with the wideband BP method and the DCS-SOMP method. In terms of computational efficiency, the proposed method is as efficient as the DCS-SOMP method and more efficient than the wideband BP method. In terms of locating accuracy, the proposed method can still locate all sources when the signal to noise ratio (SNR) is − 20 dB, while the wideband BP method and the DCS-SOMP method can only locate all sources when the SNR is higher than 0 dB. The performance of the proposed method can be improved by expanding the frequency range. Moreover, there is no extra source in the maps of the proposed method, even though the target sparsity is overestimated. Finally, a gas leak experiment is conducted to verify the feasibility of the DCS-SOMP-SVD method in the practical engineering environment. The experimental results show that the proposed method can locate both two leak sources in different frequency ranges. This research proposes a DCS-SOMP-SVD method which has sufficient robustness and low computational cost for wideband acoustic imaging.