Three-dimensional acoustic imaging with planar microphone arrays and compressive sensing

• Extend CS to three-dimensional acoustic imaging.
• Analyze the effectiveness and the limitations of CS for obtaining acoustic maps.
• Compared with CBF and TIKR, CS can suppress side lobes and enhance main lobes.
• CS in three-dimensional acoustic imaging has less computational cost than CBF.
• Conduct experiments to verify the validity of CS in the practical applications.

For obtaining super-resolution source maps, we extend compressive sensing (CS) to three-dimensional acoustic imaging. Source maps are simulated with a planar microphone array and a CS algorithm. Comparing the source maps of the CS algorithm with those of the conventional beamformer (CBF) and Tikhonov Regularization (TIKR), we find that the CS algorithm is computationally more effective and can obtain much higher resolution source maps than the CBF and TIKR. The effectiveness of the CS algorithm is analyzed. The CS algorithm can locate the sound sources exactly when the frequency is above 4000 Hz and the signal-to-noise ratio (SNR) is above 12 dB. The location error of the CS algorithm increases as the frequency drops below the threshold, and the errors in location and power increase as SNR decreases. The further from the array the source is, the larger the location error is. The lateral resolution of the CS algorithm is much better than the range resolution. Finally, experimental measurements are conducted in a semi-anechoic room. Two mobile phones are served as sound sources. The results show that the CS algorithm can reconstruct two sound sources near the bottom of the two mobile phones where the speakers are located. The feasibility of the CS algorithm is also validated with the experiment.