Department of Mathematics
Fourier method for recovering acoustic sources from multi-frequency far-field data
We consider an inverse source problem of determining a source term in the Helmholtz equation from multi-frequency far-field measurements. Based on the Fourier series expansion, we develop a novel non-iterative reconstruction method for solving the problem. A promising feature of this method is that it utilizes the data from only a few observation directions for each frequency. Theoretical uniqueness and stability analysis are provided. Numerical experiments are conducted to illustrate the effectiveness and efficiency of the proposed method in both two and three dimensions.
inverse source problem, Helmholtz equation, Fourier expansion, multi-frequency, far-field
Source Publication Title
The work of X Wang was supported by the NSFC grant under No. 11671113. The work of Y Guo was supported by the NSFC grants under Nos. 11671111, 11601107 and 41474102. The work of D Zhang was supported by the NSFC grants under No. 11671170. The work of H Liu was supported by the FRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Funds, No. 12302415, and the NSFC grant under No. 11371115.
Link to Publisher's Edition
Wang, Xianchao, Yukun Guo, Deyue Zhang, and Hongyu Liu. "Fourier method for recovering acoustic sources from multi-frequency far-field data." Inverse Problems 33.3 (2017): 035001.