Fourier method for recovering acoustic sources from multi-frequency far-field data. (1st February 2017)

• Record Type: Journal Article
• Authors: Wang, Xianchao; Guo, Yukun; Zhang, Deyue; Liu, Hongyu
• Is Part Of: Inverse problems. Volume 33:Number 3(2017:Mar.)
• Publication Date: 2017-02-01
• Subjects: inverse source problem -- Helmholtz equation -- Fourier expansion -- multi-frequency -- far-field; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa573c
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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.