An iteratively reweighted time-domain acoustic method for reconstructing the transient acoustic field

Abstract

An improved iterative reweighted least-squares based on real-time near-field acoustic hologram method (RTNAH) is proposed to reconstruct the transient acoustic field. First, time-domain convolution relation formula between the pressure time-wavenumber spectra on the hologram and reconstruction planes is first established by an impulse response function, and the corresponding matrix equation is obtained. Then, for solving the pressure spectra on the reconstruction plane, an improved iterative reweighted least-squares algorithm is applied for solving the minimization problem of the sum of 2-norm residual and 2-norm weighted solution under the weighted and sparse representation framework. By controlling the iteratively updated weighting matrix, the sparsity of the solution is promoted. Finally, the pressure spectra of the reconstruction plane are estimated, and the corresponding time-varying pressures are acquired by the two-dimensional inverse Fourier transform. A numerical simulation is conducted to observe the reconstruction capacity of the proposed method. The simulation results demonstrate that the proposed method can reconstruct the transient acoustic field in time-space domains very well. Meanwhile, several vital parameters are discussed, and the superiorities of the proposed method are testified by comparing to RTNAH with Tikhonov regularization and YALL1 model. An experiment is implemented for further validating the effectivity of the proposed method.