Acoustic Imaging with Compressed Sensing and Microphone Arrays

Abstract

This work studies the acoustic imaging problem with compressed sensing (CS) and microphone arrays. The CS algorithm with Basis Pursuit (BP) algorithm has shown satisfying results in acoustic imaging, the maps of which are characterized by super-resolution. However, the performance of the CS algorithm with the BP algorithm is limited to Restricted Isometry Property (RIP), and the algorithm has a long CPU-time. We propose a new CS algorithm with Orthogonal Matching Pursuit (OMP) algorithm for acoustic imaging. The performance of the OMP algorithm with regard to RIP is examined through numerical simulation in this work. The simulation results and CPU-time for OMP algorithm are compared with those of the BP algorithm and the conventional beamformer (CBF). When the RIP does not hold, satisfying results can still be obtained by the OMP algorithm, and the CPU-time for OMP algorithm is far less than BP algorithm. In order to validate the feasibility of the OMP algorithm in acoustic imaging, an experiment is also conducted in a semi-anechoic room. Two mobile phones are served as sound sources. We investigate the mobile phones sources and compare the experimental results with those of BP algorithm and CBF method. The OMP algorithm can locate the main sources at low frequencies, while the CBF method can just give a rough indication and fails for low frequencies due to the width of its main lobe. Due to many reconstructed sources outside of the expected source positions existing on the map, the BP algorithm fails to locate the main sources at low frequencies.