Application of compressive sensing to equivalent source method on near-field acoustic holography

Abstract

Near-field acoustic holography (NAH) is an acoustic visualization technique that uses a microphone array to measure the radiated sound waves from a source in the near-field. In the present study, the equivalent source method (ESM) and the 2D spatial Fourier transform based on the generalized discrete Fourier series (GDFS) are compared, and the reconstruction performance of NAH using compressed sensing (CS) combined with both theories for NAH measurements is discussed. Additionally, the influence of different array designs (regular and pseudo-random) on the reconstruction performance of NAH is investigated. Simulations and experimentation are used to demonstrate its feasibility. In the simulation, three source models (dipole, longitudinal quadrupole and simply supported rectangular plate) are tested over a range of frequencies, SNR and reconstruction distances. The consequence indicates that use of GDFS results in a large reconstruction error in all test conditions under the rectangular array, especially in the high frequency range. The combination of a pseudo-random array and ESM-L1 provides the best reconstruction performance in most test conditions. In the experiment, two sets of pseudo-random microphone arrays with different diameters were used. They were tested separately for the dual loudspeakers and vibrating plate. ESM-L1 is suitable for reconstructing sound fields with sparse source distributions, whereas ESM-L2 is suitable for reconstructing sound fields with continuous source distributions, such as the radiated acoustic field of a vibrating plate. However, the use of pseudo-random arrays in combination with ESM is indeed a better solution for NAH.