Compressive nonstationary near-field acoustic holography for reconstructing the instantaneous sound field

A compressive nonstationary near-field acoustic holography based on time-domain plane wave superposition method is proposed to precisely reconstruct the instantaneous sound field using the fewer measurement points. In the proposed method, by means of an instantaneous propagation kernel, a time-domain convolution superposition formula is established for relating the timevariant pressure of the hologram plane to the pressure time-wavenumber spectra of the virtual source plane. Next, compressed sensing theory and sparse representation framework are introduced into the time-marching solving inverse process of the established formula, and the smoothed l0 norm and revised Newton optimization algorithm are employed to solve the serious cumulative ill-posed problem over time for acquiring the pressure time-wavenumber spectra. The key is to approximately replace the discontinuous l0 norm by using a suitable continuous function, and the revised Newton algorithm is applied to minimize the continuous function for obtaining the optimal solution. Finally, with the aid of a time-domain convolution formula, the solved pressure time-wavenumber spectra are employed to calculate the time-variant pressure on the reconstruction plane. The proposed method not only can evidently suppress the ill-posed problem of time-marching solving inverse process for improving the reconstruction accuracy, but also can greatly reduce the measurement points and microphone number for drastically decreasing the measurement cost on the premise of ensuring the reconstruction accuracy and spatial resolution. A numerical simulation is conducted, and the simulation effects prove that the proposed method can accurately reconstruct the instantaneous sound field with the fewer measurement points in time-space domains. The reconstruction results are also compared to those of time-domain plane wave superposition method with Tikhonov regularization to verify the superiority of the proposed method with fewer measurement points under different parameter configurations. An experiment of an impaction steel plate is implemented for further validating the competence of the proposed method.