Multi-frequency angular spectrum method of moments for two-dimensional inverse source problem

Based on Fourier transform, the angular spectrum equation and its discrete model of the inverse source problem of the two-dimensional Helmholtz equation are derived. By transforming the two-dimensional inverse source problem in the spatial domain into the inverse source problem in the one-dimensional Fourier domain, the source intensity angular spectrum vector in the Fourier domain is calculated by the one-dimensional method of moments. Then, using the discrete Fourier inverse transform, a multi-frequency angular spectrum method of moments is proposed to reconstruct the inverse source problem of the two-dimensional Helmholtz equation. The reconstruction accuracy and stability of this method are improved by optimizing the excitation wavenumber sequence. Simulation calculations show that the multi-frequency angular spectrum method of moments has high reconstruction accuracy and anti-noise ability, and can also design the reconstruction model according to the effective frequency band of the acoustic sensor to achieve the highest resolution. In addition, since the calculation of the coefficient matrix of the proposed method is independent of the distribution of the source intensity function and does not require regularization processing, when the size and resolution of the required source intensity distribution area are determined, after the coefficient matrix is calculated and saved, the source intensity function corresponding to the region of interest can be reconstructed according to different sound pressure detection data, with high calculation accuracy and efficiency.