A Sparse Real Time Acoustic Holography Method for Nonstationary Acoustic Source Reconstruction

Abstract

A sparse real-time near-field acoustic holography method is proposed to precisely and stably reconstruct a transient sound field. In the proposed method, by using a time-domain impulse response function, a time domain convolution equation between the time-wavenumber pressure spectra on the hologram and reconstruction planes is first established. Then, for obtaining the time-wavenumber pressure spectrum on the reconstruction plane, a smoothed <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{0}$</tex> -norm optimization algorithm is applied to solve the serious ill-conditioned problem in the inverse process. The key of solving this problem is to approximate replace the discontinuous <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\ell_{0}$</tex> -norm by using a suitable continuous Gaussian function family, and the steepest ascent algorithm is introduced to minimize the continuous function for obtaining the optimal solution. Finally, the pressure time-wavenumber spectra on the reconstruction plane at all wavenumbers for all times are solved, and the corresponding time-dependent pressures are acquired by the two-dimensional inverse Fourier transform. A numerical simulation with a baffled planar piston is conducted to observe the performance of the proposed method. The simulation results prove that the proposed method can accurately reconstruct the transient sound field. The reconstruction results are also compared to those of real-time near-field acoustic holography with Tikhonov regularization and YALL1 modal to verify the superiority of the proposed method.